Deck 9: Exponential and Logarithmic Functions

ملء الشاشة (f)
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سؤال
Identify the horizontal asymptote of g(x)=(78)x+7g ( x ) = \left( \frac { 7 } { 8 } \right) ^ { x } + 7 .

A) y=778y = 7 \frac { 7 } { 8 }
B)x -axis
C) y=-7
D) y=7
E) y=78y = - \frac { 7 } { 8 }
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سؤال
Match f(x)=4x1f ( x ) = 4 ^ { x } - 1 with its graph.

A)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Identify the horizontal asymptote of g(x)=4x+2g ( x ) = 4 ^ { x + 2 } .

A)x -axis
B) y=2
C) y=-2
D) y=16
E) y=-16
سؤال
Sketch the graph of the function f(x)=8xf ( x ) = 8 ^ { - x } .

A)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.01)3tt=3\begin{array} { c } 10,000 ( 1.01 ) ^ { 3 t } \\t = 3\end{array}

A)10,303.010
B)10,936.853
C)91,999.387
D)4702.847
E)90,900.000
سؤال
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.7xx=1\begin{aligned}G ( x ) & = 1.7 ^ { - x } \\x & = - 1\end{aligned}

A)-0.588
B)0.588
C)2.700
D)1.700
E)-1.700
سؤال
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.5xx=1\begin{aligned}G ( x ) & = 1.5 ^ { - x } \\x & = 1\end{aligned}

A)0.500
B)0.667
C)2.500
D)-0.667
E)-1.500
سؤال
Match f(x)=3xf ( x ) = - 3 ^ { x } with its graph.

A)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
ex+6ex\frac { e ^ { x + 6 } } { e ^ { x } }

A) 1+e6x1 + e ^ { 6 - x }
B) e6e ^ { 6 }
C) e1+6xe^{1 + \frac { 6 } { x }}
D) 1+e6x1 + e ^ { \frac { 6 } { x } }
E)cannot be simplified
سؤال
Evaluate the expression 626 ^ { \sqrt { 2 } } . Round your answer to three decimal places.

A)8.485
B)3.000
C)12.603
D)2.449
E)22.274
سؤال
Simplify the expression. (4ex)3\left( 4 e ^ { x } \right) ^ { 3 }

A) 64e3x64 e ^ { 3 x }
B) 4e3x4 e ^ { 3 x }
C) 4ex34 e ^ { x ^ { 3 } }
D) 12e3x12 e ^ { 3 x }
E) 64ex364 e ^ { x ^ { 3 } }
سؤال
Simplify the expression. 5e6x- 5 e ^ { - 6 x }

A) 5e6x5 e ^ { 6 x }
B) 5e6x- \frac { 5 } { e ^ { 6 x } }
C) 5e6x- 5 \sqrt [ 6 x ] { e }
D) 5e6x\frac { 5 } { e ^ { 6 x } }
E) 5e6x\sqrt [ 6 x ] { - 5 e }
سؤال
Simplify the expression. 8x8x18 ^ { x } \cdot 8 ^ { x - 1 }

A) 82x18 ^ { 2 x - 1 }
B) 64x2x64 ^ { x ^ { 2 } - x }
C) 18\frac { 1 } { 8 }
D) 8x8 ^ { x }
E) 8x2x8 ^ { x ^ { 2 } - x }
سؤال
Evaluate the function as indicated. Round to three decimal places if necessary.
10,000(1.07)4tt=1\begin{array}{ c}10,000 ( 1.07 ) ^ { 4 t } \\ t = 1\end{array}

A)13,107.960
B)1310.796
C)10,700.000
D)42,800.000
E)44,076.205
سؤال
Evaluate the function as indicated. Round to three decimal places if necessary.

10,000(1.09)3tt=5.5\begin{array}{c} 10,000 ( 1.09 ) ^ { 3 t }\\t = 5.5\end{array}

A)212,352.559
B)227981.657
C)16,063.706
D)41,451.210
E)179,850.000
سؤال
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=50e0.1xx=20\begin{aligned}g ( x ) & = 50 e ^ { - 0.1 x } \\x & = - 20\end{aligned}

A)-6.767
B)6.767
C)-904.837
D)369.453
E)210.588
سؤال
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=100e0.5xx=8\begin{aligned}g ( x ) & = 100 e ^ { - 0.5 x } \\x & = 8\end{aligned}

A)-1087.313
B)1.832
C)5459.815
D)1.593
E)-485.225
سؤال
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=70e0.5xx=4\begin{aligned}g ( x ) & = 70 e ^ { - 0.5 x } \\x & = 4\end{aligned}

A)-9.473
B)10.705
C)-169.829
D)9.473
E)517.234
سؤال
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.7xx=3\begin{aligned}G ( x ) & = 1.7 ^ { - x } \\x & = \sqrt { 3 }\end{aligned}

A)0.399
B)-2.944
C)-0.032
D)2.507
E)not a real number
سؤال
Identify the horizontal asymptote of h(x)=12(15x)h ( x ) = \frac { 1 } { 2 } \left( 15 ^ { - x } \right) .

A) y=12y = \frac { 1 } { 2 }
B) y=130y = \frac { 1 } { 30 }
C) y=115y = \frac { 1 } { 15 }
D) y=15
E)x -axis
سؤال
After t years, the remaining mass y (in grams)of 24 grams of a radioactive elements whose half-life is 30 years is given by y=24(12)t/30,t0y = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 30 } , t \geq 0 . How much of the initial mass remains after 50 years? Round your answers to two decimal places.

A)7.56 grams
B)14.40 grams
C)3.17 grams
D)16.44 grams
E)nothing remains
سؤال
The population P (in millions)of the United States from 1970 to 2000 can be approximated by the exponential function P(t)=203.0(1.0107)tP ( t ) = 203.0 ( 1.0107 ) ^ { t } , where t is the time in years with t=0t = 0 corresponding to 1970. Use the model to estimate the population in the year 2,005. Round your answer to one decimal place. Source: U.S. Census Bureau

A)205.2 million
B)7,181.0 million
C)223.9million
D)294.6 million
E)1.5 million
سؤال
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x+5f ( x ) = 4 x + 5 and g(x)=x2g ( x ) = x - 2 .

A) 4x+34 x + 3
B) 4x23x104 x ^ { 2 } - 3 x - 10
C) 4x34 x - 3
D) 5x+35 x + 3
E) 4x28x+54 x ^ { 2 } - 8 x + 5
سؤال
Determine the principal P (to the nearest cent)that will yield a balance of <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded once per year. Round the answer to two decimal places.</strong> A)$56,306.31 B)$568,181.82 C)$68,460.62 D)$55,625.00 E)$38,461.03 <div style=padding-top: 35px> dollars when invested at rate <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded once per year. Round the answer to two decimal places.</strong> A)$56,306.31 B)$568,181.82 C)$68,460.62 D)$55,625.00 E)$38,461.03 <div style=padding-top: 35px> for 40 years, compounded once per year. Round the answer to two decimal places.

A)$56,306.31
B)$568,181.82
C)$68,460.62
D)$55,625.00
E)$38,461.03
سؤال
The value of a piece of property doubles every 16 years. You buy the property for $50,000. Its value t years after the date of purchase should be V(t)=50,000(2)t/16V ( t ) = 50,000 ( 2 ) ^ { t / 16 } . Use the model to approximate (to the nearest thousand dollars)the value of the property after 4 years.

A)$50,000
B)$6,400,000
C)$75,000
D)$59,000
E)$100,000
سؤال
Determine the principal P (to the nearest cent)that will yield a balance of A=500,000A = 500,000 dollars when invested at rate r=8.5%r = 8.5 \% for 40 years, compounded continuously. Round the answer to two decimal places.

A)$611,887.72
B)$495,364.63
C)$16,686.63
D)$13,015.58
E)$13,608.96
سؤال
Determine the principal P (to the nearest cent)that will yield a balance of A=500,000A = 500,000 dollars when invested at rate r=6.5%r = 6.5 \% for 40 years, compounded 12 times per year. Round the answer to two decimal places.

A)$973.96
B)$273,927.55
C)$16,025.64
D)$37,398.27
E)$402,834.63
سؤال
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 <div style=padding-top: 35px> , compounded 365 times per year. Round the answer to two decimal places.

A)$9,855.00
B)$8,042.90
C)$7,378.81
D)$6,027.12
E)$7,377.99
سؤال
Find (fg)(4)( f \circ g ) ( 4 ) where f(x)=5x+9f ( x ) = 5 x + 9 and g(x)=x5g ( x ) = x - 5 .

A)24
B)-29
C)4
D)28
E)-11
سؤال
Identify the transformation of f(x)=2xf ^ { \prime } ( x ) = 2 ^ { x } . h(x)=2x6h ( x ) = 2 ^ { x - 6 }

A)a shift of 6 units downward
B)a shift of 6 units to the left
C)a reflection about the line x=6
D)a shift of 6 units to the right
E)a shift of 6 units upward
سؤال
Find (gf)(3)( g \circ f ) ( 3 ) where f(x)=5x+2f ( x ) = 5 x + 2 and g(x)=x5g ( x ) = x - 5 .

A)12
B)15
C)-28
D)-8
E)-34
سؤال
Find (fg)(x)( f \circ g ) ( x ) where f(x)=6x+9f ( x ) = 6 x + 9 and g(x)=x7g ( x ) = x - 7 .

A) 6x+26 x + 2
B) 6x336 x - 33
C) 6x233x636 x ^ { 2 } - 33 x - 63
D) 6x242x+96 x ^ { 2 } - 42 x + 9
E) 7x+337 x + 33
سؤال
Determine the principal P (to the nearest cent)that will yield a balance of A=2,500,000A = 2,500,000 dollars when invested at rate r=10%r = 10 \% for 40 years, compounded 365 times per year. Round the answer to two decimal places.

A)$38,920.73
B)$1,541,095.89
C)$1,712.33
D)$2,472,756.03
E)$45,814.19
سؤال
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 <div style=padding-top: 35px> , compounded continuously. Round the answer to two decimal places.

A)$8,154.85
B)$10,950.00
C)$8,153.73
D)$8,887.56
E)$6,030.15
سؤال
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 <div style=padding-top: 35px> , compounded one time per year. Round the answer to two decimal places.

A)$33,000.00
B)$4,781.23
C)$3,000.00
D)$6,000.00
E)$7,781.23
سؤال
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 <div style=padding-top: 35px> , compounded 12 times per year. Round the answer to two decimal places.

A)$529.94
B)$4,700.00
C)$1,126.10
D)$1,004.83
E)$6,359.33
سؤال
Find (fg)(x)( f \circ g ) ( x ) where f(x)=2x+6f ( x ) = 2 x + 6 and g(x)=x22g ( x ) = x ^ { 2 } - 2 .

A) 2x312x24x122 x ^ { 3 } 12 x ^ { 2 } - 4 x - 12
B) 2x2+22 x ^ { 2 } + 2
C) 4x2+24x+344 x ^ { 2 } + 24 x + 34
D) 4x2+44 x ^ { 2 } + 4
E) 2x2+42 x ^ { 2 } + 4
سؤال
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 <div style=padding-top: 35px> dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 <div style=padding-top: 35px> for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 <div style=padding-top: 35px> , compounded 4 times per year. Round the answer to two decimal places.

A)$3,161.40
B)$12,000.00
C)$12,645.59
D)$94,298.50
E)$6,392.88
سؤال
Identify the transformation of f(x)=15xf ( x ) = 15 ^ { x } . h(x)=15xh ( x ) = - 15 ^ { x }

A)a reflection about the y -axis
B)a reflection about the x -axis
C)a reflection about the line y=-x
D)a reflection about the line y=x
E)a reflection about the line x=15
سؤال
Determine the principal P (to the nearest cent)that will yield a balance of <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded 4 times per year. Round the answer to two decimal places.</strong> A)$173,611.11 B)$14,218.75 C)$1,026,614.38 D)$147,569.44 E)$71,090.14 <div style=padding-top: 35px> dollars when invested at rate <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded 4 times per year. Round the answer to two decimal places.</strong> A)$173,611.11 B)$14,218.75 C)$1,026,614.38 D)$147,569.44 E)$71,090.14 <div style=padding-top: 35px> for 40 years, compounded 4 times per year. Round the answer to two decimal places.

A)$173,611.11
B)$14,218.75
C)$1,026,614.38
D)$147,569.44
E)$71,090.14
سؤال
Use the function of f(x)={(2,3),(1,1),(0,0),(1,1),(2,3)}f ( x ) = \{ ( - 2,3 ) , ( - 1,1 ) , ( 0,0 ) , ( 1 , - 1 ) , ( 2 , - 3 ) \} and g(x)={(3,2),(1,3),(0,3),(2,4),(3,4)}g ( x ) = \{ ( - 3 , - 2 ) , ( - 1 , - 3 ) , ( 0,3 ) , ( 2,4 ) , ( 3,4 ) \} to find the value of (gf)(2)( g \circ f ) ( - 2 ) .

A)4
B)3
C)-3
D)2
E)-2
سؤال
Find the inverse function of f(x)=6xf ( x ) = 6 - x .

A) f1(x)=6xf ^ { - 1 } ( x ) = 6 - x
B) f1(x)=6xf ^ { - 1 } ( x ) = - 6 - x
C) f1(x)=6f ^ { - 1 } ( x ) = 6
D) f1(x)=6+xf ^ { - 1 } ( x ) = 6 + x
E) f1(x)=6+xf ^ { - 1 } ( x ) = - 6 + x
سؤال
Find the inverse function of f(x)=47xf ( x ) = 4 - 7 x .

A) f1(x)=17x4f ^ { - 1 } ( x ) = \frac { 1 } { 7 } x - 4
B) f1(x)=4x7f ^ { - 1 } ( x ) = \frac { 4 - x } { 7 }
C) f1(x)=17x+4f ^ { - 1 } ( x ) = \frac { 1 } { 7 } x + 4
D) f1(x)=x47f ^ { - 1 } ( x ) = \frac { x - 4 } { 7 }
E)The function does not have an inverse.
سؤال
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.
 <strong>Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.    f ( x ) = \sqrt { 81 - x ^ { 2 } } </strong> A)f is one-to-one B)f is not one-to-one C)cannot be determined <div style=padding-top: 35px>
f(x)=81x2f ( x ) = \sqrt { 81 - x ^ { 2 } }

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
سؤال
Which statement(s)verify that f(x)=4x+1f ( x ) = \frac { 4 } { x + 1 } and g(x)=4xxg ( x ) = \frac { 4 - x } { x } are inverse?

A) f(x)+g(x)=4x+1+4xx=0f ( x ) + g ( x ) = \frac { 4 } { x + 1 } + \frac { 4 - x } { x } = 0
B) f(x)g(x)=4x+14xx=1\frac { f ( x ) } { g ( x ) } = \frac { \frac { 4 } { x + 1 } } { \frac { 4 - x } { x } } = 1
C) f(g(x))=44xx+1=x,g(f(x))=44x+14x+1=xf ( g ( x ) ) = \frac { 4 } { \frac { 4 - x } { x } + 1 } = x , g ( f ( x ) ) = \frac { 4 - \frac { 4 } { x + 1 } } { \frac { 4 } { x + 1 } } = x
D) f(x)+g(x)=4x+1+4xx=1f ( x ) + g ( x ) = \frac { 4 } { x + 1 } + \frac { 4 - x } { x } = 1
E) f(g(x))=44xx+1=1;g(f(x))=4x+14x+1=1f ( g ( x ) ) = \frac { 4 } { \frac { 4 - x } { x } + 1 } = 1 ; g ( f ( x ) ) = \frac { \frac { 4 } { x + 1 } } { \frac { 4 } { x + 1 } } = 1
سؤال
Find the domain of gfg \circ f where f(x)=xx5f ( x ) = \frac { x } { x - 5 } and g(x)=xg ( x ) = \sqrt { x } .

A) [0,5)(5,)[ 0,5 ) \cup ( 5 , \infty )
B) (25,)( 25 , \infty )
C) (,0](5,)( - \infty , 0 ] \cup ( 5 , \infty )
D) [0,25)(25,)[ 0,25 ) \cup ( 25 , \infty )
E) (,25)(25,)( - \infty , 25 ) \cup ( 25 , \infty )
سؤال
Find the domain of gfg \circ f where f(x)=x2f ( x ) = \sqrt { x - 2 } and g(x)=x+6g ( x ) = x + 6 .

A) [2,)[ 2 , \infty )
B) [4,)[ 4 , \infty )
C) [4,)[ - 4 , \infty )
D) [6,)[ - 6 , \infty )
E) [0,)[ 0 , \infty )
سؤال
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.
 <strong>Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.    f ( x ) = 5 \sqrt { - x } </strong> A)f is one-to-one B)f is not one-to-one C)cannot be determined <div style=padding-top: 35px>
f(x)=5xf ( x ) = 5 \sqrt { - x }

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
سؤال
Which statement(s)verify that f(x)=9x1f ( x ) = 9 x - 1 and g(x)=19(x+1)g ( x ) = \frac { 1 } { 9 } ( x + 1 ) are inverse?

A) f(x)g(x)=(9x1)19(x+1)=1f ( x ) \cdot g ( x ) = ( 9 x - 1 ) \frac { 1 } { 9 } ( x + 1 ) = - 1
B) f(g(x))=(9(19x)+1)1=x,g(f(x))=19(9(x1)+1)=xf ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x , g ( f ( x ) ) = \frac { 1 } { 9 } ( 9 ( x - 1 ) + 1 ) = x
C) f(g(x))=(9(19x)+1)1=x;g(f(x))=19((9x1)+1)=xf ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x
D) f(g(x))=9(19(x+1))1=x;g(f(x))=19((9x1)+1)=xf ( g ( x ) ) = 9 \left( \frac { 1 } { 9 } ( x + 1 ) \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x
E) f(x)g(x)=9(x1)9(x+1)=1\frac { f ( x ) } { g ( x ) } = \frac { 9 ( x - 1 ) } { 9 ( x + 1 ) } = - 1
سؤال
Find (gf)(5)( g \circ f ) ( - 5 ) where f(x)=3x+4f ( x ) = 3 x + 4 and g(x)=x26g ( x ) = x ^ { 2 } - 6 .

A)73
B)115
C)223
D)61
E)-9
سؤال
Find the domain of gfg \circ f where f(x)=xx64f ( x ) = \frac { x } { x - 64 } and g(x)=xg ( x ) = \sqrt { x } .

A) (0,64](64,)( 0,64 ] \cup ( 64 , \infty )
B) (,0](64,)( - \infty , 0 ] \cup ( 64 , \infty )
C) [0,8)(8,)[ 0,8 ) \cup ( 8 , \infty )
D) (0,)( 0 , \infty )
E) (0,)( 0 , \infty ) .
سؤال
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x+7f ( x ) = 4 x + 7 and g(x)=x21g ( x ) = x ^ { 2 } - 1 .

A) 4x328x24x74 x ^ { 3 } 28 x ^ { 2 } - 4 x - 7
B) 4x2+34 x ^ { 2 } + 3
C) 16x2+56x+4816 x ^ { 2 } + 56 x + 48
D) 16x2+616 x ^ { 2 } + 6
E) 4x2+64 x ^ { 2 } + 6
سؤال
Find the inverse function of f(t)=t75f ( t ) = t ^ { 7 } - 5 .

A) f1(t)=t57f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t - 5 }
B) f1(t)=t75f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } - 5
C) f1(t)=t+57f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t + 5 }
D) f1(t)=t7+5f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } + 5
E)The function does not have an inverse.
سؤال
Find the domain of fgf \circ g where f(x)=x7f ( x ) = \sqrt { x - 7 } and g(x)=x+5g ( x ) = x + 5 .

A) [5,)[ - 5 , \infty )
B) [0,)[ 0 , \infty )
C) [7,)[ 7 , \infty )
D) [2,)[ - 2 , \infty )
E) [2,)[ 2 , \infty )
سؤال
Find (gf)(3)( g \circ f ) ( 3 ) where f(x)=2x11f ( x ) = 2 x - 11 and g(x)=x+6g ( x ) = \sqrt { x + 6 } .

A)-16
B)2
C)1
D)-15
E)-5
سؤال
Find (fg)(3)( f \circ g ) ( 3 ) where f(x)=2x38f ( x ) = 2 x - 38 and g(x)=x+33g ( x ) = \sqrt { x + 33 } .

A)-64
B)-26
C)-5
D)-192
E)1
سؤال
Which statement(s)verify that f(x)=x+47f ( x ) = \sqrt [ 7 ] { x + 4 } and g(x)=x24g ( x ) = x ^ { 2 } - 4 are inverse?

A) f(g(x))=x74+47=x;g(f(x))=(x7)7+44=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } - 4 + 4 } = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x } ) ^ { 7 } + 4 - 4 = x
B) f(x)g(x)=x+47(x74)=xf ( x ) \cdot g ( x ) = \sqrt [ 7 ] { x + 4 } \cdot \left( x ^ { 7 } - 4 \right) = x
C) f(g(x))=x774+4=x;g(f(x))=(x+47)74=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } } - 4 + 4 = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x + 4 } ) ^ { 7 } - 4 = x
D) f(g(x))=x74+47=x;g(f(x))=(x+47)74=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } - 4 + 4 } = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x + 4 } ) ^ { 7 } - 4 = x
E) f(x)g(x)=x+47x7b=1\frac { f ( x ) } { g ( x ) } = \frac { \sqrt [ 7 ] { x + 4 } } { x ^ { 7 } - b } = - 1
سؤال
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x8f ( x ) = 4 x - 8 and g(x)=x+4g ( x ) = \sqrt { x + 4 } .

A) 4x44 \sqrt { x - 4 }
B) 4x4\sqrt { 4 x - 4 }
C) 4x+168\sqrt { 4 x + 16 } - 8
D) (4x8)x+4( 4 x - 8 ) \sqrt { x + 4 }
E) 4x+484 \sqrt { x + 4 } - 8
سؤال
Find (fg)(x)( f \circ g ) ( x ) where f(x)=4x3f ( x ) = 4 x - 3 and g(x)=x+8g ( x ) = \sqrt { x + 8 } .

A) 4x+834 \sqrt { x + 8 } - 3
B) 4x+5\sqrt { 4 x + 5 }
C) 4x+323\sqrt { 4 x + 32 } - 3
D) 4x+54 \sqrt { x + 5 }
E) (4x3)x+8( 4 x - 3 ) \sqrt { x + 8 }
سؤال
Find (fg)(3)( f \circ g ) ( - 3 ) where f(x)=4x+6f ( x ) = 4 x + 6 and g(x)=x24g ( x ) = x ^ { 2 } - 4 .

A)32
B)38
C)146
D)132
E)26
سؤال
Match f(x)=log2(x+3)f ( x ) = \log _ { 2 } ( x + 3 ) with its graph.

A)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Match f(x)=log4(x)f ( x ) = \log _ { 4 } ( - x ) with its graph.

A)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Write the exponential equation 7292/3=81729 ^ { 2 / 3 } = 81 in logarithmic form.

A) log72981=23\log _ { 729 } 81 = \frac { 2 } { 3 }
B) log9729=9\log _ { 9 } 729 = 9
C) log981=2\log _ { 9 } 81 = 2
D) log72981=32\log _ { 729 } 81 = \frac { 3 } { 2 }
E) log72981=3\log _ { 729 } 81 = 3
سؤال
Identify the vertical asymptote of g(t)=log5tg ( t ) = - \log _ { 5 } t .

A) t=5
B) t=15t = - \frac { 1 } { 5 }
C) t=15t = \frac { 1 } { 5 }
D) t=-5
E)y -axis
سؤال
Evaluate the logarithm. log6416\log _ { 64 } 16

A) 12\frac { 1 } { 2 }
B) 3
C) 2
D) 23\frac { 2 } { 3 }
E) log6416\log _ { 64 } 16 is undefined.
سؤال
Use a calculator to evaluate the common logarithm log1047\log _ { 10 } 47 . Round your answer to four decimal places.

A)1.6812
B)1.6721
C)3.8501
D)1.9777
E)3.8712
سؤال
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Find the inverse function of f(x)=x+5,x5f ( x ) = \sqrt { x + 5 } , x \geq - 5 .

A) f1(x)=x25,x0f ^ { - 1 } ( x ) = x ^ { 2 } - 5 , x \geq 0
B) f1(x)=x225,x0f ^ { - 1 } ( x ) = x ^ { 2 } - 25 , x \geq 0
C) f1(x)=(x25)2f ^ { - 1 } ( x ) = ( x - 25 ) ^ { 2 }
D) f1(x)=(x5)2f ^ { - 1 } ( x ) = ( x - 5 ) ^ { 2 }
E)The function does not have an inverse.
سؤال
Evaluate the logarithm. log9(0)\log _ { 9 } ( 0 )

A) 19\frac { 1 } { 9 }
B)1
C) -1
D)0
E)Undefined
سؤال
Identify the vertical asymptote of g(t)=6+log7tg ( t ) = - 6 + \log _ { 7 } t .

A) t=-6
B) t=6
C) t=7
D) t=-7
E)y -axis
سؤال
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate the logarithm. log36216\log _ { 36 } 216

A) 32\frac { 3 } { 2 }
B)3
C) 23\frac { 2 } { 3 }
D)6
E) log36216\log _ { 36 } 216 is undefined.
سؤال
Match f(x)=3+log5xf ( x ) = 3 + \log _ { 5 } x with its graph.

A)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Match f(x)=log2xf ( x ) = - \log _ { 2 } x with its graph.

A)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate the logarithm. log3[27]\log _ { 3 } [ 27 ]

A) -3
B)9
C) log327\log _ { 3 } 27
D)3
E) log327\log _ { 3 } 27 is undefined.
سؤال
Evaluate the logarithm. log6(6)\log _ { 6 } ( - 6 )

A)0
B) 16\frac { 1 } { 6 }
C) -1
D) e1e^ { - 1 }
E) log6(6)\log _ { 6 } ( - 6 ) is undefined.
سؤال
Write the logarithmic equation log2132=5\log _ { 2 } \frac { 1 } { 32 } = - 5 in exponential form.

A) 25=1322 ^ { - 5 } = \frac { 1 } { 32 }
B) 25=1322 ^ { - 5 } = - \frac { 1 } { 32 }
C) 52=1105 ^ { 2 } = \frac { 1 } { 10 }
D) 52=325 ^ { 2 } = 32
E) 25=152 ^ { - 5 } = \frac { 1 } { 5 }
سؤال
Evaluate the logarithm. log51125\log _ { 5 } \frac { 1 } { 125 }

A) 3\sqrt { 3 }
B) -3
C)0
D) 13\frac { 1 } { 3 }
E) log51125\log _ { 5 } \frac { 1 } { 125 } is undefined.
سؤال
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
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Deck 9: Exponential and Logarithmic Functions
1
Identify the horizontal asymptote of g(x)=(78)x+7g ( x ) = \left( \frac { 7 } { 8 } \right) ^ { x } + 7 .

A) y=778y = 7 \frac { 7 } { 8 }
B)x -axis
C) y=-7
D) y=7
E) y=78y = - \frac { 7 } { 8 }
y=7
2
Match f(x)=4x1f ( x ) = 4 ^ { x } - 1 with its graph.

A)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = 4 ^ { x } - 1  with its graph.</strong> A)   B)   C)   D)   E)

3
Identify the horizontal asymptote of g(x)=4x+2g ( x ) = 4 ^ { x + 2 } .

A)x -axis
B) y=2
C) y=-2
D) y=16
E) y=-16
x -axis
4
Sketch the graph of the function f(x)=8xf ( x ) = 8 ^ { - x } .

A)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
B)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
C)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
D)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
E)  <strong>Sketch the graph of the function  f ( x ) = 8 ^ { - x }  .</strong> A)   B)   C)   D)   E)
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5
Evaluate the function as indicated. Round to three decimal places if necessary. 10,000(1.01)3tt=3\begin{array} { c } 10,000 ( 1.01 ) ^ { 3 t } \\t = 3\end{array}

A)10,303.010
B)10,936.853
C)91,999.387
D)4702.847
E)90,900.000
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6
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.7xx=1\begin{aligned}G ( x ) & = 1.7 ^ { - x } \\x & = - 1\end{aligned}

A)-0.588
B)0.588
C)2.700
D)1.700
E)-1.700
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7
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.5xx=1\begin{aligned}G ( x ) & = 1.5 ^ { - x } \\x & = 1\end{aligned}

A)0.500
B)0.667
C)2.500
D)-0.667
E)-1.500
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8
Match f(x)=3xf ( x ) = - 3 ^ { x } with its graph.

A)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = - 3 ^ { x }  with its graph.</strong> A)   B)   C)   D)   E)
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9
ex+6ex\frac { e ^ { x + 6 } } { e ^ { x } }

A) 1+e6x1 + e ^ { 6 - x }
B) e6e ^ { 6 }
C) e1+6xe^{1 + \frac { 6 } { x }}
D) 1+e6x1 + e ^ { \frac { 6 } { x } }
E)cannot be simplified
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10
Evaluate the expression 626 ^ { \sqrt { 2 } } . Round your answer to three decimal places.

A)8.485
B)3.000
C)12.603
D)2.449
E)22.274
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11
Simplify the expression. (4ex)3\left( 4 e ^ { x } \right) ^ { 3 }

A) 64e3x64 e ^ { 3 x }
B) 4e3x4 e ^ { 3 x }
C) 4ex34 e ^ { x ^ { 3 } }
D) 12e3x12 e ^ { 3 x }
E) 64ex364 e ^ { x ^ { 3 } }
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12
Simplify the expression. 5e6x- 5 e ^ { - 6 x }

A) 5e6x5 e ^ { 6 x }
B) 5e6x- \frac { 5 } { e ^ { 6 x } }
C) 5e6x- 5 \sqrt [ 6 x ] { e }
D) 5e6x\frac { 5 } { e ^ { 6 x } }
E) 5e6x\sqrt [ 6 x ] { - 5 e }
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13
Simplify the expression. 8x8x18 ^ { x } \cdot 8 ^ { x - 1 }

A) 82x18 ^ { 2 x - 1 }
B) 64x2x64 ^ { x ^ { 2 } - x }
C) 18\frac { 1 } { 8 }
D) 8x8 ^ { x }
E) 8x2x8 ^ { x ^ { 2 } - x }
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14
Evaluate the function as indicated. Round to three decimal places if necessary.
10,000(1.07)4tt=1\begin{array}{ c}10,000 ( 1.07 ) ^ { 4 t } \\ t = 1\end{array}

A)13,107.960
B)1310.796
C)10,700.000
D)42,800.000
E)44,076.205
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15
Evaluate the function as indicated. Round to three decimal places if necessary.

10,000(1.09)3tt=5.5\begin{array}{c} 10,000 ( 1.09 ) ^ { 3 t }\\t = 5.5\end{array}

A)212,352.559
B)227981.657
C)16,063.706
D)41,451.210
E)179,850.000
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16
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=50e0.1xx=20\begin{aligned}g ( x ) & = 50 e ^ { - 0.1 x } \\x & = - 20\end{aligned}

A)-6.767
B)6.767
C)-904.837
D)369.453
E)210.588
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17
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=100e0.5xx=8\begin{aligned}g ( x ) & = 100 e ^ { - 0.5 x } \\x & = 8\end{aligned}

A)-1087.313
B)1.832
C)5459.815
D)1.593
E)-485.225
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18
Evaluate the function as indicated. Round your answer to three decimal places. g(x)=70e0.5xx=4\begin{aligned}g ( x ) & = 70 e ^ { - 0.5 x } \\x & = 4\end{aligned}

A)-9.473
B)10.705
C)-169.829
D)9.473
E)517.234
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19
Evaluate the function as indicated. Round your answer to three decimal places. G(x)=1.7xx=3\begin{aligned}G ( x ) & = 1.7 ^ { - x } \\x & = \sqrt { 3 }\end{aligned}

A)0.399
B)-2.944
C)-0.032
D)2.507
E)not a real number
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20
Identify the horizontal asymptote of h(x)=12(15x)h ( x ) = \frac { 1 } { 2 } \left( 15 ^ { - x } \right) .

A) y=12y = \frac { 1 } { 2 }
B) y=130y = \frac { 1 } { 30 }
C) y=115y = \frac { 1 } { 15 }
D) y=15
E)x -axis
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21
After t years, the remaining mass y (in grams)of 24 grams of a radioactive elements whose half-life is 30 years is given by y=24(12)t/30,t0y = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 30 } , t \geq 0 . How much of the initial mass remains after 50 years? Round your answers to two decimal places.

A)7.56 grams
B)14.40 grams
C)3.17 grams
D)16.44 grams
E)nothing remains
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22
The population P (in millions)of the United States from 1970 to 2000 can be approximated by the exponential function P(t)=203.0(1.0107)tP ( t ) = 203.0 ( 1.0107 ) ^ { t } , where t is the time in years with t=0t = 0 corresponding to 1970. Use the model to estimate the population in the year 2,005. Round your answer to one decimal place. Source: U.S. Census Bureau

A)205.2 million
B)7,181.0 million
C)223.9million
D)294.6 million
E)1.5 million
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23
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x+5f ( x ) = 4 x + 5 and g(x)=x2g ( x ) = x - 2 .

A) 4x+34 x + 3
B) 4x23x104 x ^ { 2 } - 3 x - 10
C) 4x34 x - 3
D) 5x+35 x + 3
E) 4x28x+54 x ^ { 2 } - 8 x + 5
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24
Determine the principal P (to the nearest cent)that will yield a balance of <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded once per year. Round the answer to two decimal places.</strong> A)$56,306.31 B)$568,181.82 C)$68,460.62 D)$55,625.00 E)$38,461.03 dollars when invested at rate <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded once per year. Round the answer to two decimal places.</strong> A)$56,306.31 B)$568,181.82 C)$68,460.62 D)$55,625.00 E)$38,461.03 for 40 years, compounded once per year. Round the answer to two decimal places.

A)$56,306.31
B)$568,181.82
C)$68,460.62
D)$55,625.00
E)$38,461.03
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25
The value of a piece of property doubles every 16 years. You buy the property for $50,000. Its value t years after the date of purchase should be V(t)=50,000(2)t/16V ( t ) = 50,000 ( 2 ) ^ { t / 16 } . Use the model to approximate (to the nearest thousand dollars)the value of the property after 4 years.

A)$50,000
B)$6,400,000
C)$75,000
D)$59,000
E)$100,000
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26
Determine the principal P (to the nearest cent)that will yield a balance of A=500,000A = 500,000 dollars when invested at rate r=8.5%r = 8.5 \% for 40 years, compounded continuously. Round the answer to two decimal places.

A)$611,887.72
B)$495,364.63
C)$16,686.63
D)$13,015.58
E)$13,608.96
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27
Determine the principal P (to the nearest cent)that will yield a balance of A=500,000A = 500,000 dollars when invested at rate r=6.5%r = 6.5 \% for 40 years, compounded 12 times per year. Round the answer to two decimal places.

A)$973.96
B)$273,927.55
C)$16,025.64
D)$37,398.27
E)$402,834.63
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28
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 365 times per year. Round the answer to two decimal places.</strong> A)$9,855.00 B)$8,042.90 C)$7,378.81 D)$6,027.12 E)$7,377.99 , compounded 365 times per year. Round the answer to two decimal places.

A)$9,855.00
B)$8,042.90
C)$7,378.81
D)$6,027.12
E)$7,377.99
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29
Find (fg)(4)( f \circ g ) ( 4 ) where f(x)=5x+9f ( x ) = 5 x + 9 and g(x)=x5g ( x ) = x - 5 .

A)24
B)-29
C)4
D)28
E)-11
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30
Identify the transformation of f(x)=2xf ^ { \prime } ( x ) = 2 ^ { x } . h(x)=2x6h ( x ) = 2 ^ { x - 6 }

A)a shift of 6 units downward
B)a shift of 6 units to the left
C)a reflection about the line x=6
D)a shift of 6 units to the right
E)a shift of 6 units upward
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31
Find (gf)(3)( g \circ f ) ( 3 ) where f(x)=5x+2f ( x ) = 5 x + 2 and g(x)=x5g ( x ) = x - 5 .

A)12
B)15
C)-28
D)-8
E)-34
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32
Find (fg)(x)( f \circ g ) ( x ) where f(x)=6x+9f ( x ) = 6 x + 9 and g(x)=x7g ( x ) = x - 7 .

A) 6x+26 x + 2
B) 6x336 x - 33
C) 6x233x636 x ^ { 2 } - 33 x - 63
D) 6x242x+96 x ^ { 2 } - 42 x + 9
E) 7x+337 x + 33
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33
Determine the principal P (to the nearest cent)that will yield a balance of A=2,500,000A = 2,500,000 dollars when invested at rate r=10%r = 10 \% for 40 years, compounded 365 times per year. Round the answer to two decimal places.

A)$38,920.73
B)$1,541,095.89
C)$1,712.33
D)$2,472,756.03
E)$45,814.19
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34
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded continuously. Round the answer to two decimal places.</strong> A)$8,154.85 B)$10,950.00 C)$8,153.73 D)$8,887.56 E)$6,030.15 , compounded continuously. Round the answer to two decimal places.

A)$8,154.85
B)$10,950.00
C)$8,153.73
D)$8,887.56
E)$6,030.15
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35
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded one time per year. Round the answer to two decimal places.</strong> A)$33,000.00 B)$4,781.23 C)$3,000.00 D)$6,000.00 E)$7,781.23 , compounded one time per year. Round the answer to two decimal places.

A)$33,000.00
B)$4,781.23
C)$3,000.00
D)$6,000.00
E)$7,781.23
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36
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 12 times per year. Round the answer to two decimal places.</strong> A)$529.94 B)$4,700.00 C)$1,126.10 D)$1,004.83 E)$6,359.33 , compounded 12 times per year. Round the answer to two decimal places.

A)$529.94
B)$4,700.00
C)$1,126.10
D)$1,004.83
E)$6,359.33
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37
Find (fg)(x)( f \circ g ) ( x ) where f(x)=2x+6f ( x ) = 2 x + 6 and g(x)=x22g ( x ) = x ^ { 2 } - 2 .

A) 2x312x24x122 x ^ { 3 } 12 x ^ { 2 } - 4 x - 12
B) 2x2+22 x ^ { 2 } + 2
C) 4x2+24x+344 x ^ { 2 } + 24 x + 34
D) 4x2+44 x ^ { 2 } + 4
E) 2x2+42 x ^ { 2 } + 4
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38
Determine the balance A ( to the nearest cent)for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 dollars invested at a rate <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 for <strong>Determine the balance A ( to the nearest cent)for   dollars invested at a rate   for   , compounded 4 times per year. Round the answer to two decimal places.</strong> A)$3,161.40 B)$12,000.00 C)$12,645.59 D)$94,298.50 E)$6,392.88 , compounded 4 times per year. Round the answer to two decimal places.

A)$3,161.40
B)$12,000.00
C)$12,645.59
D)$94,298.50
E)$6,392.88
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39
Identify the transformation of f(x)=15xf ( x ) = 15 ^ { x } . h(x)=15xh ( x ) = - 15 ^ { x }

A)a reflection about the y -axis
B)a reflection about the x -axis
C)a reflection about the line y=-x
D)a reflection about the line y=x
E)a reflection about the line x=15
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40
Determine the principal P (to the nearest cent)that will yield a balance of <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded 4 times per year. Round the answer to two decimal places.</strong> A)$173,611.11 B)$14,218.75 C)$1,026,614.38 D)$147,569.44 E)$71,090.14 dollars when invested at rate <strong>Determine the principal P (to the nearest cent)that will yield a balance of   dollars when invested at rate   for 40 years, compounded 4 times per year. Round the answer to two decimal places.</strong> A)$173,611.11 B)$14,218.75 C)$1,026,614.38 D)$147,569.44 E)$71,090.14 for 40 years, compounded 4 times per year. Round the answer to two decimal places.

A)$173,611.11
B)$14,218.75
C)$1,026,614.38
D)$147,569.44
E)$71,090.14
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41
Use the function of f(x)={(2,3),(1,1),(0,0),(1,1),(2,3)}f ( x ) = \{ ( - 2,3 ) , ( - 1,1 ) , ( 0,0 ) , ( 1 , - 1 ) , ( 2 , - 3 ) \} and g(x)={(3,2),(1,3),(0,3),(2,4),(3,4)}g ( x ) = \{ ( - 3 , - 2 ) , ( - 1 , - 3 ) , ( 0,3 ) , ( 2,4 ) , ( 3,4 ) \} to find the value of (gf)(2)( g \circ f ) ( - 2 ) .

A)4
B)3
C)-3
D)2
E)-2
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42
Find the inverse function of f(x)=6xf ( x ) = 6 - x .

A) f1(x)=6xf ^ { - 1 } ( x ) = 6 - x
B) f1(x)=6xf ^ { - 1 } ( x ) = - 6 - x
C) f1(x)=6f ^ { - 1 } ( x ) = 6
D) f1(x)=6+xf ^ { - 1 } ( x ) = 6 + x
E) f1(x)=6+xf ^ { - 1 } ( x ) = - 6 + x
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43
Find the inverse function of f(x)=47xf ( x ) = 4 - 7 x .

A) f1(x)=17x4f ^ { - 1 } ( x ) = \frac { 1 } { 7 } x - 4
B) f1(x)=4x7f ^ { - 1 } ( x ) = \frac { 4 - x } { 7 }
C) f1(x)=17x+4f ^ { - 1 } ( x ) = \frac { 1 } { 7 } x + 4
D) f1(x)=x47f ^ { - 1 } ( x ) = \frac { x - 4 } { 7 }
E)The function does not have an inverse.
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44
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.
 <strong>Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.    f ( x ) = \sqrt { 81 - x ^ { 2 } } </strong> A)f is one-to-one B)f is not one-to-one C)cannot be determined
f(x)=81x2f ( x ) = \sqrt { 81 - x ^ { 2 } }

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
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45
Which statement(s)verify that f(x)=4x+1f ( x ) = \frac { 4 } { x + 1 } and g(x)=4xxg ( x ) = \frac { 4 - x } { x } are inverse?

A) f(x)+g(x)=4x+1+4xx=0f ( x ) + g ( x ) = \frac { 4 } { x + 1 } + \frac { 4 - x } { x } = 0
B) f(x)g(x)=4x+14xx=1\frac { f ( x ) } { g ( x ) } = \frac { \frac { 4 } { x + 1 } } { \frac { 4 - x } { x } } = 1
C) f(g(x))=44xx+1=x,g(f(x))=44x+14x+1=xf ( g ( x ) ) = \frac { 4 } { \frac { 4 - x } { x } + 1 } = x , g ( f ( x ) ) = \frac { 4 - \frac { 4 } { x + 1 } } { \frac { 4 } { x + 1 } } = x
D) f(x)+g(x)=4x+1+4xx=1f ( x ) + g ( x ) = \frac { 4 } { x + 1 } + \frac { 4 - x } { x } = 1
E) f(g(x))=44xx+1=1;g(f(x))=4x+14x+1=1f ( g ( x ) ) = \frac { 4 } { \frac { 4 - x } { x } + 1 } = 1 ; g ( f ( x ) ) = \frac { \frac { 4 } { x + 1 } } { \frac { 4 } { x + 1 } } = 1
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46
Find the domain of gfg \circ f where f(x)=xx5f ( x ) = \frac { x } { x - 5 } and g(x)=xg ( x ) = \sqrt { x } .

A) [0,5)(5,)[ 0,5 ) \cup ( 5 , \infty )
B) (25,)( 25 , \infty )
C) (,0](5,)( - \infty , 0 ] \cup ( 5 , \infty )
D) [0,25)(25,)[ 0,25 ) \cup ( 25 , \infty )
E) (,25)(25,)( - \infty , 25 ) \cup ( 25 , \infty )
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47
Find the domain of gfg \circ f where f(x)=x2f ( x ) = \sqrt { x - 2 } and g(x)=x+6g ( x ) = x + 6 .

A) [2,)[ 2 , \infty )
B) [4,)[ 4 , \infty )
C) [4,)[ - 4 , \infty )
D) [6,)[ - 6 , \infty )
E) [0,)[ 0 , \infty )
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48
Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.
 <strong>Use the horizontal Line Test to determine if the function is one-to-one and so has an inverse function.    f ( x ) = 5 \sqrt { - x } </strong> A)f is one-to-one B)f is not one-to-one C)cannot be determined
f(x)=5xf ( x ) = 5 \sqrt { - x }

A)f is one-to-one
B)f is not one-to-one
C)cannot be determined
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49
Which statement(s)verify that f(x)=9x1f ( x ) = 9 x - 1 and g(x)=19(x+1)g ( x ) = \frac { 1 } { 9 } ( x + 1 ) are inverse?

A) f(x)g(x)=(9x1)19(x+1)=1f ( x ) \cdot g ( x ) = ( 9 x - 1 ) \frac { 1 } { 9 } ( x + 1 ) = - 1
B) f(g(x))=(9(19x)+1)1=x,g(f(x))=19(9(x1)+1)=xf ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x , g ( f ( x ) ) = \frac { 1 } { 9 } ( 9 ( x - 1 ) + 1 ) = x
C) f(g(x))=(9(19x)+1)1=x;g(f(x))=19((9x1)+1)=xf ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x
D) f(g(x))=9(19(x+1))1=x;g(f(x))=19((9x1)+1)=xf ( g ( x ) ) = 9 \left( \frac { 1 } { 9 } ( x + 1 ) \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x
E) f(x)g(x)=9(x1)9(x+1)=1\frac { f ( x ) } { g ( x ) } = \frac { 9 ( x - 1 ) } { 9 ( x + 1 ) } = - 1
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50
Find (gf)(5)( g \circ f ) ( - 5 ) where f(x)=3x+4f ( x ) = 3 x + 4 and g(x)=x26g ( x ) = x ^ { 2 } - 6 .

A)73
B)115
C)223
D)61
E)-9
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51
Find the domain of gfg \circ f where f(x)=xx64f ( x ) = \frac { x } { x - 64 } and g(x)=xg ( x ) = \sqrt { x } .

A) (0,64](64,)( 0,64 ] \cup ( 64 , \infty )
B) (,0](64,)( - \infty , 0 ] \cup ( 64 , \infty )
C) [0,8)(8,)[ 0,8 ) \cup ( 8 , \infty )
D) (0,)( 0 , \infty )
E) (0,)( 0 , \infty ) .
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52
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x+7f ( x ) = 4 x + 7 and g(x)=x21g ( x ) = x ^ { 2 } - 1 .

A) 4x328x24x74 x ^ { 3 } 28 x ^ { 2 } - 4 x - 7
B) 4x2+34 x ^ { 2 } + 3
C) 16x2+56x+4816 x ^ { 2 } + 56 x + 48
D) 16x2+616 x ^ { 2 } + 6
E) 4x2+64 x ^ { 2 } + 6
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53
Find the inverse function of f(t)=t75f ( t ) = t ^ { 7 } - 5 .

A) f1(t)=t57f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t - 5 }
B) f1(t)=t75f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } - 5
C) f1(t)=t+57f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t + 5 }
D) f1(t)=t7+5f ^ { - 1 } ( t ) = \sqrt [ 7 ] { t } + 5
E)The function does not have an inverse.
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54
Find the domain of fgf \circ g where f(x)=x7f ( x ) = \sqrt { x - 7 } and g(x)=x+5g ( x ) = x + 5 .

A) [5,)[ - 5 , \infty )
B) [0,)[ 0 , \infty )
C) [7,)[ 7 , \infty )
D) [2,)[ - 2 , \infty )
E) [2,)[ 2 , \infty )
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55
Find (gf)(3)( g \circ f ) ( 3 ) where f(x)=2x11f ( x ) = 2 x - 11 and g(x)=x+6g ( x ) = \sqrt { x + 6 } .

A)-16
B)2
C)1
D)-15
E)-5
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56
Find (fg)(3)( f \circ g ) ( 3 ) where f(x)=2x38f ( x ) = 2 x - 38 and g(x)=x+33g ( x ) = \sqrt { x + 33 } .

A)-64
B)-26
C)-5
D)-192
E)1
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57
Which statement(s)verify that f(x)=x+47f ( x ) = \sqrt [ 7 ] { x + 4 } and g(x)=x24g ( x ) = x ^ { 2 } - 4 are inverse?

A) f(g(x))=x74+47=x;g(f(x))=(x7)7+44=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } - 4 + 4 } = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x } ) ^ { 7 } + 4 - 4 = x
B) f(x)g(x)=x+47(x74)=xf ( x ) \cdot g ( x ) = \sqrt [ 7 ] { x + 4 } \cdot \left( x ^ { 7 } - 4 \right) = x
C) f(g(x))=x774+4=x;g(f(x))=(x+47)74=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } } - 4 + 4 = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x + 4 } ) ^ { 7 } - 4 = x
D) f(g(x))=x74+47=x;g(f(x))=(x+47)74=xf ( g ( x ) ) = \sqrt [ 7 ] { x ^ { 7 } - 4 + 4 } = x ; g ( f ( x ) ) = ( \sqrt [ 7 ] { x + 4 } ) ^ { 7 } - 4 = x
E) f(x)g(x)=x+47x7b=1\frac { f ( x ) } { g ( x ) } = \frac { \sqrt [ 7 ] { x + 4 } } { x ^ { 7 } - b } = - 1
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58
Find (gf)(x)( g \circ f ) ( x ) where f(x)=4x8f ( x ) = 4 x - 8 and g(x)=x+4g ( x ) = \sqrt { x + 4 } .

A) 4x44 \sqrt { x - 4 }
B) 4x4\sqrt { 4 x - 4 }
C) 4x+168\sqrt { 4 x + 16 } - 8
D) (4x8)x+4( 4 x - 8 ) \sqrt { x + 4 }
E) 4x+484 \sqrt { x + 4 } - 8
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59
Find (fg)(x)( f \circ g ) ( x ) where f(x)=4x3f ( x ) = 4 x - 3 and g(x)=x+8g ( x ) = \sqrt { x + 8 } .

A) 4x+834 \sqrt { x + 8 } - 3
B) 4x+5\sqrt { 4 x + 5 }
C) 4x+323\sqrt { 4 x + 32 } - 3
D) 4x+54 \sqrt { x + 5 }
E) (4x3)x+8( 4 x - 3 ) \sqrt { x + 8 }
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60
Find (fg)(3)( f \circ g ) ( - 3 ) where f(x)=4x+6f ( x ) = 4 x + 6 and g(x)=x24g ( x ) = x ^ { 2 } - 4 .

A)32
B)38
C)146
D)132
E)26
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61
Match f(x)=log2(x+3)f ( x ) = \log _ { 2 } ( x + 3 ) with its graph.

A)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = \log _ { 2 } ( x + 3 )  with its graph.</strong> A)   B)   C)   D)   E)
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62
Match f(x)=log4(x)f ( x ) = \log _ { 4 } ( - x ) with its graph.

A)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = \log _ { 4 } ( - x )  with its graph.</strong> A)   B)   C)   D)   E)
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63
Write the exponential equation 7292/3=81729 ^ { 2 / 3 } = 81 in logarithmic form.

A) log72981=23\log _ { 729 } 81 = \frac { 2 } { 3 }
B) log9729=9\log _ { 9 } 729 = 9
C) log981=2\log _ { 9 } 81 = 2
D) log72981=32\log _ { 729 } 81 = \frac { 3 } { 2 }
E) log72981=3\log _ { 729 } 81 = 3
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64
Identify the vertical asymptote of g(t)=log5tg ( t ) = - \log _ { 5 } t .

A) t=5
B) t=15t = - \frac { 1 } { 5 }
C) t=15t = \frac { 1 } { 5 }
D) t=-5
E)y -axis
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65
Evaluate the logarithm. log6416\log _ { 64 } 16

A) 12\frac { 1 } { 2 }
B) 3
C) 2
D) 23\frac { 2 } { 3 }
E) log6416\log _ { 64 } 16 is undefined.
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66
Use a calculator to evaluate the common logarithm log1047\log _ { 10 } 47 . Round your answer to four decimal places.

A)1.6812
B)1.6721
C)3.8501
D)1.9777
E)3.8712
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67
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
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68
Find the inverse function of f(x)=x+5,x5f ( x ) = \sqrt { x + 5 } , x \geq - 5 .

A) f1(x)=x25,x0f ^ { - 1 } ( x ) = x ^ { 2 } - 5 , x \geq 0
B) f1(x)=x225,x0f ^ { - 1 } ( x ) = x ^ { 2 } - 25 , x \geq 0
C) f1(x)=(x25)2f ^ { - 1 } ( x ) = ( x - 25 ) ^ { 2 }
D) f1(x)=(x5)2f ^ { - 1 } ( x ) = ( x - 5 ) ^ { 2 }
E)The function does not have an inverse.
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69
Evaluate the logarithm. log9(0)\log _ { 9 } ( 0 )

A) 19\frac { 1 } { 9 }
B)1
C) -1
D)0
E)Undefined
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70
Identify the vertical asymptote of g(t)=6+log7tg ( t ) = - 6 + \log _ { 7 } t .

A) t=-6
B) t=6
C) t=7
D) t=-7
E)y -axis
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71
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
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72
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
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73
Evaluate the logarithm. log36216\log _ { 36 } 216

A) 32\frac { 3 } { 2 }
B)3
C) 23\frac { 2 } { 3 }
D)6
E) log36216\log _ { 36 } 216 is undefined.
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74
Match f(x)=3+log5xf ( x ) = 3 + \log _ { 5 } x with its graph.

A)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = 3 + \log _ { 5 } x  with its graph.</strong> A)   B)   C)   D)   E)
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75
Match f(x)=log2xf ( x ) = - \log _ { 2 } x with its graph.

A)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
B)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
C)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
D)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
E)  <strong>Match  f ( x ) = - \log _ { 2 } x  with its graph.</strong> A)   B)   C)   D)   E)
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76
Evaluate the logarithm. log3[27]\log _ { 3 } [ 27 ]

A) -3
B)9
C) log327\log _ { 3 } 27
D)3
E) log327\log _ { 3 } 27 is undefined.
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77
Evaluate the logarithm. log6(6)\log _ { 6 } ( - 6 )

A)0
B) 16\frac { 1 } { 6 }
C) -1
D) e1e^ { - 1 }
E) log6(6)\log _ { 6 } ( - 6 ) is undefined.
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78
Write the logarithmic equation log2132=5\log _ { 2 } \frac { 1 } { 32 } = - 5 in exponential form.

A) 25=1322 ^ { - 5 } = \frac { 1 } { 32 }
B) 25=1322 ^ { - 5 } = - \frac { 1 } { 32 }
C) 52=1105 ^ { 2 } = \frac { 1 } { 10 }
D) 52=325 ^ { 2 } = 32
E) 25=152 ^ { - 5 } = \frac { 1 } { 5 }
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79
Evaluate the logarithm. log51125\log _ { 5 } \frac { 1 } { 125 }

A) 3\sqrt { 3 }
B) -3
C)0
D) 13\frac { 1 } { 3 }
E) log51125\log _ { 5 } \frac { 1 } { 125 } is undefined.
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80
Match the graph with the graph of its inverse function. <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)

A) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
B) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
C) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
D) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
E) <strong>Match the graph with the graph of its inverse function.  </strong> A)   B)   C)   D)   E)
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