Deck 1: Graphs, Functions, and Models

Question 1

Find the domain and range of the function represented in the graph.

A)Domain: (-∞,∞); Range:[-5,∞)
B)Domain: (-∞,∞); Range: (-∞,∞)
C)Domain:[4,∞); Range:[-5,∞)
D)Domain: (-∞,4) or (4,∞); Range: (-∞,-5) or (-5,∞)

Answer 1

Domain: (-∞,∞); Range:[-5,∞)

Question 2

Graph the function.
$$f ( x ) = \sqrt { x + 3 }$$

A)
B)
C)
D)

Answer 2

C

Question 3

Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right
triangle.
(9,-4),(13,-4),(13,3)

A) Yes
B) No

Answer 3

A

Question 4

Find the domain of the function.
f(x)=-7 x+7

A) $\{ x \mid x > 0 \} , \text { or } ( 0 , \infty )$
B) all real numbers, or $( - \infty , \infty )$
C) $\{ x \mid x \neq 0 \} , \text { or } ( - \infty , 0 ) \cup ( 0 , \infty )$
D) $\{ x \mid x > - 7 \} , \text { or } ( - 7 , \infty )$

Question 5

Graph the equation.
$$y = x ^ { 2 } + 6 x + 5$$

A)
B)
C)
D)

Question 6

Tell whether or not the relation is a function.
{(-3,9), (-1,4), (2,-6), (6,-9)}

A) Yes
B) No

Question 7

Solve the problem.
Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with an embroidery of a Great Pyrenees dog on the front. There are fixed costs of $670 to set up for production, and variable costs of $44 per jacket. Write an equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x jackets.

A) C(x) = 670x + 44
B) C(x) = 670 - 44x
C) C(x) = 670 + 44x
D) C(x) = (670 + 44) x

Question 8

Solve the problem.
The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. By using linear regression, the following function is obtained: y=67.3+1.07 x where x is number of hours studied and y is score on the test. Use this function to predict the score on the test of a student who studies 11 hours.
$\begin{array} { l | r r r r r r } \text { Hours } & 5 & 10 & 4 & 6 & 10 & 9 \\\hline \text { Score } & 64 & 86 & 69 & 86 & 59 & 87\end{array}$

A) 74.1
B) 79.1
C) 83.8
D) 84.1

Question 9

Find the domain and range of the function represented in the graph.

A) Domain: $[ - \pi , 2 \pi ]$ Range: [-3,3]
B) Domain: $[ 0,2 \pi ]$ Range: [0,3]
C) Domain: $[ \pi , 2 \pi ]$ Range: [-4,2]
D) Domain: [-3,3] ; Range: $[ - \pi , 2 \pi ]$

Question 10

Solve the problem.
Find the average rate of change.

A)$4.00per year
B)-$3.00per year
C)-$4.00per year
D)$3.00per year

Question 11

Solve the problem.
The function h described by $h ( t ) = - 16 t ^ { 2 } + 33.1 t + 124.26$ gives the height of a ball thrown upward with a speed of 33.1 feet per second from a 124.26ft high window t seconds after it is thrown until it hits the ground. Find the height of the ball 1.4 seconds after it is thrown.

A) 139.24 ft
B) 201.96 ft
C) 109.28 ft
D) 46.56 ft

Question 12

Determine the domain and range of the relation.
{(7,1),(8,4),(-3,3),(-3,2)}

A) Domain: {7,-3,8,-3} ; Range: {1,3,4,2}
B) Domain: {1,3,4,2} ; Range: {7,-3,8}
C) Domain: {7,-3,8} ; Range: {1,3,4,2}
D) Domain: {7,-3,8,3} ; Range: {1,3,4,2}

Question 13

Solve the problem using your calculator.
The paired data below consist of the costs of advertising (in thousands of dollars)and the number of products sold (in thousands). Use a graphing calculator to model the data with a linear function that predicts the number of products sold as a function of the cost of advertising.
$\begin{array} { c | r r r r r r r r } \text { Cost } & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \\\hline \text { Number } & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73\end{array}$

A) y=-26.4-1.42 x
B) y=26.4+1.42 x
C) y=55.8-2.79 x
D) y=55.8+2.79 x

Question 14

Find the zero of the linear function.
f(x)=-4 x+5

A) -1
B) 1
C) $\frac { 5 } { 4 }$
D) $- \frac { 4 } { 5 }$

Question 15

Graph the circle using the given equation.

A)
B)
C)
D)

Question 16

Solve the problem.
$x ^ { 2 } + ( y + 9 ) ^ { 2 } = 16$

A) (0,-9) ; 4
B) (0,9) ; 4
C) (-9,0) ; 16
D) (9,0) ; 16

Question 17

Find the zero of the linear function.
f(x)= 4 +9x

A) $- \frac { 9 } { 4 }$
B) $- \frac { 4 } { 9 }$
C) $\frac { 9 } { 4 }$
D) $\frac { 4 } { 9 }$

Question 18

Determine whether the graph is the graph of a function.

A) Yes
B) No

Question 19

Find the equation of the circle. Express the equation in standard form

A) $( x - 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1 ^ { 2 }$
B) $( x + 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 1 ^ { 2 }$
C) $( x + 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 1 ^ { 2 }$
D) $( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 1 ^ { 2 }$

Question 20

Solve the problem.
To convert a temperature from degrees Celsius to degrees Fahrenheit, you multiply the temperature in degrees Celsius by 1.8 and then add 32 to the result. Express F as a linear function of

A) F(c)= 33.8c
B) $F ( c ) = \frac { c - 32 } { 1.8 }$
C) F(c)=1.8c+32
D) F(c)=1.8+32c

Question 21

Find the slope of the line containing the given points.
f(8.3)= 6.5 and f(-11.6)=-7.9

A) $- \frac { 144 } { 199 }$
B) $\frac { 199 } { 144 }$
C) $- \frac { 199 } { 144 }$
D) $\frac { 144 } { 199 }$

Question 22

Solve the equation.
7x-(2 x-1)=2

A) $\frac { 1 } { 5 }$
B) $- \frac { 1 } { 9 }$
C) $\frac { 1 } { 9 }$
D) $- \frac { 1 } { 5 }$

Question 23

Solve the problem.
Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with a embroidery of a Great Pyrenees dog on the front. There are fixed costs of $680 to set up for production, and variable
Costs of $43 per jacket. Write an equation that can be used to determine the total cost, C(x),
Encountered by Marty's Company in producing x jackets, and use the equation to find the total cost
Of producing 90 jackets.

A)$4562
B)$4542
C)$4530
D)$4550

Question 24

Find the zero of the linear function.
f(x)=11-x

A) -11
B) 11
C) 1
D) -22

Question 25

Solve the equation.
3(4 x+6)=2(x+6)

A) $- \frac { 3 } { 7 }$
B) $- \frac { 3 } { 5 }$
C) -6
D) 10

Question 26

Determine whether the pair of lines is parallel, perpendicular, or neither.
3x-8 y=18
32 x+12 y=18

A) Parallel
B) Perpendicular
C) Neither

Question 27

Find an equation for the circle.
Center at (0,-5) , radius 9

A) $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$
B) $( x - 5 ) ^ { 2 } + y ^ { 2 } = 81$
C) $x ^ { 2 } + ( y + 5 ) ^ { 2 } = 81$
D) $( x + 5 ) ^ { 2 } + y ^ { 2 } = 81$

Question 28

Solve the equation.
3(4 x+1)=5-5(4 x-3)

A) $- \frac { 5 } { 32 }$
B) $\frac { 5 } { 32 }$
C) $\frac { 17 } { 32 }$
D) 17

Question 29

Find the slope and the y-intercept of the line with the given equation.
5x-2y+5=0

A) $\frac { 5 } { 2 } ; \left( 0 , - \frac { 5 } { 2 } \right)$
B) $- \frac { 5 } { 2 } ; \left( 0 , - \frac { 5 } { 2 } \right)$
C) $- \frac { 5 } { 2 } ; \left( 0 , \frac { 5 } { 2 } \right)$
D) $\frac { 5 } { 2 } ; \left( 0 , \frac { 5 } { 2 } \right)$

Question 30

Solve the problem.
The function H described by H(x) =2.75x+71.48 can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose humerus is 33.8 cm long.

A) 40.43 cm
B) 164.43 cm
C) 108.03 cm
D) 21.47 cm

Question 31

Determine whether the graph is the graph of a function.

A) Yes
B) No

Question 32

Find the slope and the y-intercept of the line with the given equation.
x=11

A) not defined; no y-intercept
B) not defined; (11,0)
C) -11 ;(-11,0)
D) -11 ;(0,0)

Question 33

Solve the problem.
A car rental company charges $26 per day to rent a particular type of car and $0.16 per mile. Juan is charged $42.48 for a one-day rental. How many miles did he drive?

A)118 mi
B)103 mi
C)240 mi
D)266 mi

Question 34

Graph the equation using the slope and the y-intercept.
f(x) = 3x+2

A)
B)
C)
D)

Question 35

Solve the problem.
Company A rents copiers for a monthly charge of $90 plus 6 cents per copy. Company B rents copiers for a monthly charge of $180 plus 3 cents per copy. What is the number of copies above
Which Company A's charges are the higher of the two?

A)6000 copies
B)3000 copies
C)1500 copies
D)3100 copies

Question 36

Find the slope of the line.

A) 1
B) -1
C) 2
D) -2

Question 37

Solve the problem.
Last year, 302 million music CDs were purchased by 112 million households in the United States. On average, how many CDs were purchased in each household?

A)151 CDs
B)2.7 CDs
C)302 CDs
D)3 CDs

Question 38

Solve the problem.
The information in the chart gives the salary of a person for the stated years. Model the data with a linear function using the points (1, 24,500)and (3, 26,600). $\begin{array} { l | l } \text { Year, x } & \text { Salary, y } \\\hline 1990,0 & \$ 23,500 \\1991,1 & \$ 24,500 \\1992,2 & \$ 25,200 \\1993,3 & \$ 26,600 \\1994,4 & \$ 27,200\end{array}$

A) y=-1295 x+23,500
B) y=28.7 x+23,500
C) y=1050 x+23,500
D) y=1050x

Question 39

Determine the slope, if it exists, of the graph of the given linear equation.
f(x)=7+2 x

A) m=-2
B) m=-7
C) m=7
D) m=2

Question 40

Solve the problem.
A shipping company has determined that their drivers in Montana on average travel 80 miles on a single delivery route for mail order products. This is five times the distance of an average route for
Their drivers in New Jersey. How far, on average, is the route in New Jersey?

A)160 mi
B)400 mi
C)16 mi
D)80 mi

Question 41

Find the coordinates of the points shown on the graph.

A) C: (-3,-6) , D: (4,-6)
B) C: (-3,4) , D: (-6,2)
C) C: (-3,4) , D: (2,-6)
D) C: (4,10) , D: (-6,2)

Question 42

The following table contains input-output values for a function. Is this function linear?
$\begin{array} { r | r } \mathrm { x } & \mathrm { y } \\\hline - 4 & - 4 \\- 2 & - 16 \\2 & - 20 \\2 & - 16 \\4 & - 16 \\0 & - 20 \\2 & - 16\end{array}$

A) Yes
B) No

Question 43

Find the midpoint of the segment having the given endpoints.
(3,7) and (-4,8)

A) $\left( \frac { 7 } { 2 } , - \frac { 1 } { 2 } \right)$
B) $\left( - \frac { 1 } { 2 } , \frac { 15 } { 2 } \right)$
C) (-1,15)
D) (7,-1)

Question 44

Find the slope of the line.

A) 0
B) -5
C) not defined
D) 5

Question 45

Solve and graph the solution set.
$- 5 x + 10 \leq - 6 x - 2$

A) $\{ x \mid x \leq - 12 \} \text { or } ( - \infty , - 12 ]$


B) $\{ x \mid x > - 5 \} \text { or } ( - 5 , \infty )$


C) $\{ x \mid x < - 5 \} \text { or } ( - \infty , - 5 )$


D) $\{ x \mid x \geq - 12 \} \text { or } [ - 12 , \infty )$

Question 46

Write equations of the horizontal and the vertical lines that pass through the given point.
$\left( - 4 , \frac { 2 } { 5 } \right)$

A) horizontal: $y = - \frac { 2 } { 5 }$ vertical: x=-4
B) horizontal: y=-4 ; vertical: $x = \frac { 2 } { 5 }$
C) horizontal: $y = \frac { 2 } { 5 } x$ vertical: x=-4 y
D) horizontal: $y = \frac { 2 } { 5 }$ vertical: x=-4

Question 47

Find the slope of the line containing the given points.
(-1,7) and (-1,-9)

A) 0
B) -8
C) 1
D) not defined

Question 48

Find the slope and the y-intercept of the line with the given equation.
f(x)=-1.5+x

A) 1; (0,-1.5)
B) 1; (0,1.5)
C) -1; (0,-1.5)
D) 1 ; (-1.5,0)

Question 49

Solve the problem.
The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge of $35 for the repairman to come to the house, to which a charge of $22 per hour is added. Find an equation that can be used to determine the labor cost, C(x), of a repair that takes x hours.

A) C(x) = (35 + 22) x
B) C(x) = 35 - 22x
C) C(x) = 22 + 35x
D) C(x) = 35 + 22x

Question 50

Plot the two points given by the ordered pairs.
A(-4, -4), B(-6, 2)

A)
B)
C)
D)

Question 51

Find the intercepts and then graph the line.

A) x-intercept: (3, 0); y-intercept: (0, -6)

B) x-intercept: (-3, 0); y-intercept: (0, 6)

C) x-intercept: (3, 0); y-intercept: (0, 6)

D) x-intercept: (-3, 0); y-intercept: (0, -6)

Question 52

Solve the equation.
$\frac { 8 } { 5 } y + 5 = \frac { 3 } { 8 }$

A) $\frac { 185 } { 64 }$
В) $- \frac { 5 } { 4 }$
C) $- \frac { 11 } { 32 }$
D) $- \frac { 185 } { 64 }$

Question 53

Find the zero of the linear function.
f(x)= 22-x

A) 22
B) $\frac { 1 } { 22 }$
C)-22
D) 0

Question 54

Find the domain and range of the function represented in the graph.

A) Domain: [-5,0] ; Range: [0,5)
B) Domain: [0,5] ; Range: [0,5]
C) Domain: (0,5] ; Range: $( - 5 , \infty )$
D) Domain: (0,5) ; Range: (0,5)

Question 55

Solve the problem using your calculator.
Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below. Use a graphing calculator to model the data with a linear function that predicts a student's score on Test B as a function of his or her score on Test A.
$\begin{array} { c | c | c | c | c | c | c | c | c | c } \text { Test A } & 48 & 52 & 58 & 44 & 43 & 43 & 40 & 51 & 59 \\\hline \text { Test B } & 73 & 67 & 73 & 59 & 58 & 56 & 58 & 64 & 74\end{array}$

A) y=-19.4-0.930x
B) y=19.4+0.930x
C) y=-0.930+19.4x
D) y=0.930-19.4x

Question 56

Find the midpoint of the segment having the given endpoints.
(4,0) and (8,6)

A) (6,3)
B) (-4,-6)
C) (12,6)
D) (-2,-3)

Question 57

Solve and write interval notation for the solution set. Then graph the solution set.
$- 3 \leq \frac { 1 } { 4 } ( 3 x - 1 ) < 4$

A) $\left[ - \frac { 11 } { 3 } , \frac { 17 } { 3 } \right]$


B) $\left( - \frac { 13 } { 3 } , 5 \right]$


C) $\left[ - \frac { 13 } { 3 } , 5 \right)$


D) $\left( - \frac { 11 } { 3 } , \frac { 17 } { 3 } \right]$

Question 58

Find the distance between the pair of points. Give an exact answer, and where appropriate, an approximation to three
decimal places.
(-1,9) and (-7,12)

A) $\sqrt { 9 } , 3.000$
B) $\sqrt { 18 } , 4.243$
C) $\sqrt { 90 } , 9.487$
D) $\sqrt { 45 } , 6.708$

Question 59

Find the domain of the function.
$f ( x ) = 6 - \frac { 4 } { x }$

A) $\{ x \mid x > 6 \} \text {, or } ( 6 , \infty )$
B) $\{ x \mid x < 4 \} \text {, or } ( - \infty , 4 )$
C) all real numbers, or $( - \infty , \infty )$
D) $\{ x \mid x \neq 0 \} \text {, or } ( - \infty , 0 ) \cup ( 0 , \infty )$

Question 60

Solve the problem.
A deep sea diving bell is being lowered at a constant rate. After 12 minutes, the bell is at a depth of 500 feet. After 55 minutes the bell is at a depth of 1400 feet. What is the average rate of lowering per
Minute? Round your answer to the nearest tenth.

A)0.05 ft per min
B)25.5 ft per min
C)20.9 ft per min
D)16.4 ft per min

Question 61

Tell whether or not the relation is a function.
{(2,-7), (2,-5), (5,1), (9,-7), (10,8)}

A)Yes
B)No

Question 62

The following table contains input-output values for a function. Is this function linear?
$\begin{array} { r | r } \mathrm { x } & \mathrm { y } \\\hline 4 & 15 \\7 & 48 \\10 & 99 \\13 & 168 \\16 & 255 \\19 & 360 \\22 & 483\end{array}$

A) Yes
B) No

Question 63

Plot the two points given by the ordered pairs.
A(-1, 0), B(-2, 5)

A)
B)
C)

D)

Question 64

Use the given graph to find the x-intercept and the zero of the function.

A) (1,0); 1
B) (3,0); 3
C) (0,0); 0
D) (3,1); 3

Question 65

Is the following correspondence a function?

A)Yes
B)No

Question 66

Solve the equation.
2x-5=0

A) $- \frac { 2 } { 5 }$
B) $\frac { 5 } { 2 }$
C) $- \frac { 5 } { 2 }$
D) $\frac { 2 } { 5 }$

Question 67

Solve the equation.
-3 x+9=9-3 x

A) no solution
B) 0
C) 9
D) all real numbers

Question 68

Find the equation of the circle. Express the equation in standard form

A) $( x + 15 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 10 ^ { 2 }$
B) $( x + 15 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 10 ^ { 2 }$
C) $( x + 10 ) ^ { 2 } + ( y - 15 ) ^ { 2 } = 10 ^ { 2 }$
D) $( x + 10 ) ^ { 2 } + ( y + 15 ) ^ { 2 } = 10 ^ { 2 }$

Question 69

Determine whether the pair of lines is parallel, perpendicular, or neither.
6x+2 y=8
18 x+6 y=28

A) Parallel
B) Perpendicular
C) Neither

Question 70

Evaluate as requested.
Given that $g ( x ) = 5 x ^ { 3 }$ find g(5+h) .

A) $625 - 375 h + 50 h ^ { 2 } - 5 h ^ { 3 }$
B) $125 + 75 h + 75 h ^ { 2 } + 6 h ^ { 3 }$
C) $- 625 + 375 h - 15 h ^ { 2 } + h ^ { 3 }$
D) $625 + 375 h + 75 h ^ { 2 } + 5 h ^ { 3 }$

Question 71

Solve the problem.
Roberto invested some money at 8%, and then invested $3000 more than twice this amount at 11%. His total annual income from the two investments was $4830. How much was invested at 11%?

A)$30,000
B)$9000
C)$3300
D)$33,000

Question 72

Solve the problem.
On a recent trip, Sarah's car traveled 20 mph faster on the first 120 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

A)10 mph
B)60 mph
C)35 mph
D)40 mph

Question 73

Find the slope and the y-intercept of the line with the given equation.
$f ( x ) = - \frac { 3 } { 5 } x + 1$

A) $- \frac { 3 } { 5 } ; ( 0,1 )$
B) $\frac { 3 } { 5 } ; ( 1,0 )$
C) -1 ;(0,1)
D) 1 ;(0,1)

Question 74

Write a slope-intercept equation for a line with the given characteristics.
m = 0; passes through (7, 5)

A)x = 5
B)x = 7
C)y = 5
D)y = 7

Question 75

Determine the slope, if it exists, of the graph of the given linear equation.
$y = \frac { 1 } { 3 }$

A) m= $\frac { 1 } { 3 }$
B) m=0
C) not defined
D) m= $- \frac { 1 } { 3 }$

Question 76

Answer the question.
The points (-2,3),(1,6),(3,-2) , and (6,1) are the vertices of a quadrilateral. Is the quadrilateral a rectangle?

A) Yes
B) No

Question 77

Find an equation for the circle.
Center at (5, 0), radius 6A)
$( x - 5 ) ^ { 2 } + y ^ { 2 } = 36$
B) $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 6$
C) $x ^ { 2 } + ( y + 5 ) ^ { 2 } = 6$
D) $( x + 5 ) ^ { 2 } + y ^ { 2 } = 36$

Question 78

Find the zero of the linear function.
f(x)=4-9 x

A) $\frac { 9 } { 4 }$
B) $- \frac { 9 } { 4 }$
C) $\frac { 4 } { 9 }$
D) $- \frac { 4 } { 9 }$

Question 79

Solve the problem.
Water accounts for 60% of a man's weight. Stan weighs 174 lb. How much of his body weight is water?

A)87 lb
B)174 lb
C)104 lb
D)139 lb

Question 80

Determine whether a linear model might fit the data.

A) Yes
B) No