Deck 13: Functions

Question 1

If f ( x ) = $-$ 7| x | + 8, find f (0), f ( $-$ 4), f (2), f ( $-$ 6).

A) f (0) = 8, f ( $-$ 4) = $-$ 20, f (2) = 6, f ( $-$ 6) = $-$ 34
B) f (0) = 9, f ( $-$ 4) = $-$ 21, f (2) = 5, f ( $-$ 6) = $-$ 35
C) f (0) = 8, f ( $-$ 4) = 20, f (2) = 6, f ( $-$ 6) = 34
D) f (0) = 11, f ( $-$ 4) = $-$ 22, f (2) = 3, f ( $-$ 6) = $-$ 36

Answer 1

f (0) = 8, f ( $-$ 4) = $-$ 20, f (2) = 6, f ( $-$ 6) = $-$ 34

Question 2

If f ( x ) = 2 x + 6, find f (0), f ( $-$ 5), f (4), f ( $-$ 9).

A) f (0) = $-$ 6, f ( $-$ 5) = 4, f (4) = $-$ 14, f ( $-$ 9) = 12
B) f (0) = 7, f ( $-$ 5) = $-$ 5, f (4) = 15, f ( $-$ 9) = $-$ 13
C) f (0) = 9, f ( $-$ 5) = $-$ 6, f (4) = 17, f ( $-$ 9) = $-$ 14
D) f (0) = 6, f ( $-$ 5) = $-$ 4, f (4) = 14, f ( $-$ 9) = $-$ 12

Answer 2

f (0) = 6, f ( $-$ 5) = $-$ 4, f (4) = 14, f ( $-$ 9) = $-$ 12

Question 3

Specify the domain for the relation. {( x , y ) | 8 y $-$ 5 x = 15}

A) $D = ( 8 , \infty )$
B) $D = ( - \infty , \infty )$
C) $D = ( - \infty , 8 )$
D) $D = ( - 8,5 )$

Answer 3

$D = ( - \infty , \infty )$

Question 4

Specify the range for the relation. {(3, 1), (9, 7), (11, 12), (15, 18)}

A) R = {1, 7, 12, 18}
B) R = ( $-$ 3, 15)
C) R = {3, 9, 11, 15, 1, 7, 12, 18}
D) R = {3, 9, 11, 15}

Question 5

Specify the range for the relation. {( x , y ) | 2 x ² = 8 y ³}

A) $D = ( - \infty , \infty )$
B) $D = ( - 2,8 )$
C) $D = ( 2 , \infty )$
D) $D = ( - \infty , 2 )$

Question 6

If f ( x ) = $-$ x 2 $-$ 5 x + 6, find f (3), f ( $-$ 1), f (6), f ( $-$ 4).

A) f (3) = 0, f ( $-$ 1) = 12, f (6) = 12, f ( $-$ 4) = 42
B) f (3) = 2, f ( $-$ 1) = 15, f (6) = 14, f ( $-$ 4) = 45
C) f (3) = 1, f ( $-$ 1) = 13, f (6) = 13, f ( $-$ 4) = 43
D) f (3) = 3, f ( $-$ 1) = 14, f (6) = 15, f ( $-$ 4) = 44

Question 7

Specify the domain for the function. $f ( x ) = \sqrt { x ^ { 2 } - 4 }$

A) $D = [ 2 , \infty )$
B) $D = ( - \infty , - 2 ] \cup [ 2 , \infty )$
C) $D = [ - 2,2 ]$
D) $D = ( - \infty , - 2 ) \cup ( 2 , \infty )$

Question 8

Specify the domain for the relation. {(4, 2), (8, 5), (13, 12), (16, 17)}

A) D = {4, 8, 13, 16, 2, 5, 12, 17}
B) D = {4, 8, 13, 16}
C) D = ( $-$ 4, 16)
D) D = {2, 5, 12, 17}

Question 9

The domain of the function $f ( x ) = \sqrt { x + 5 }$ is all real numbers greater than or equal to zero.

Question 10

Specify the domain for the function. $f ( t ) = \frac { - 2 } { x ^ { 2 } + 3 }$

A) $D = ( - 3,2 )$
B) $D = ( - \infty , 3 )$
C) $D = ( - \infty , \infty )$
D) $D = ( 3 , \infty )$

Question 11

Specify the domain for the function. $h ( x ) = \frac { 1 } { x ^ { 2 } + 4 x - 32 }$

A) $D = ( - \infty , 4 ) \cup ( 4 , \infty )$
B) $D = ( - \infty , - 8 ) \cup ( - 8 , \infty )$
C) $D = ( - \infty , - 8 ) \cup ( - 8,4 ) \cup ( 4 , \infty )$
D) $D = ( - \infty , \infty )$

Question 12

A relation is a special type of function.

Question 13

Specify the domain for the function. $f ( x ) = \frac { 8 } { x - 7 }$

A) $D = ( - \infty , 7 )$
B) $D = ( - \infty , \infty )$
C) $D = ( 7 , \infty )$
D) $D = ( - \infty , 7 ) \cup ( 7 , \infty )$

Question 14

Given $g ( x ) = x ^ { 2 } - 1$ , the notation $g ( 4 )$ means to find the value of g when x is 4.

Question 15

Specify the domain for the function. f ( x ) = 2 x $-$ 8

A) $D = ( 8 , \infty )$
B) $D = ( - \infty , 8 )$
C) $D = ( - \infty , \infty )$
D) $D = ( - 8,2 )$

Question 16

Specify the domain for the function. $h ( x ) = \frac { 1 } { ( x - 3 ) ( x + 5 ) }$

A) $D = ( - \infty , 3 ) \cup ( 3 , \infty )$
B) $D = ( - \infty , - 5 ) \cup ( - 5 , \infty )$
C) $D = ( - \infty , \infty )$
D) $D = ( - \infty , - 5 ) \cup ( - 5,3 ) \cup ( 3 , \infty )$

Question 17

Specify the domain for the function. $f ( x ) = \sqrt { x ^ { 2 } + 7 x - 18 }$

A) $D = ( - \infty , - 9 ] \cup [ 2 , \infty )$
B) $D = ( - \infty , - 2 ) \cup ( 9 , \infty )$
C) $D = [ - 9,2 ]$
D) $D = [ 2 , \infty )$

Question 18

The set of all second components of the ordered pairs of a relation is called the range.

Question 19

Specify the domain for the function. $f ( x ) = \frac { - 2 } { x ^ { 2 } + 3 x }$

A) $D = ( - \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0 , \infty )$
B) $D = ( - \infty , \infty )$
C) $D = ( - \infty , 0 ) \cup ( 0 , \infty )$
D) $D = ( - \infty , - 3 ) \cup ( - 3 , \infty )$

Question 20

Specify the domain for the function. $h ( x ) = \sqrt { x + 9 }$

A) $D = [ - 9 , \infty )$
B) $D = ( - 9,9 )$
C) $D = ( 9 , \infty )$
D) $D = ( - \infty , 9 ]$

Question 21

Specify the domain for the function. Please enter your answer in interval notation.

Question 22

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x ) = $-$ x 2 $-$ 6.

A) 6 a
B) $-$ 6
C) h + a
D) $-$ 2 a $-$ h

Question 23

Specify the domain for the following relation. Please enter your answer as the numbers, separated by commas. {(1, 2), (7, 8), (14, 10), (16, 18)}

Question 24

If find .

Question 25

Specify the domain for the function. Please enter your answer in interval notation.

Question 26

Specify the domain for the function. Please enter your answer in interval notation. f ( x ) = 4 x 9

Question 27

Specify the domain for the following relation. Please enter your answer in interval notation. {( x , y ) | 9 y 7 x = 15}

Question 28

Find for f ( x ) = 3 x + 6.

Question 29

Specify the domain for the function. Please enter your answer in interval notation.

Question 30

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x ) = $-$ 9 x + 3.

A) 9 a
B) h + a
C) $-$ 9
D) $-$ 3

Question 31

Specify the range for the following relation. Please enter your answer as the numbers, separated by commas. {(2, 3), (9, 6), (12, 11), (16, 15)}

Question 32

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x ) = x 2 $-$ 5 x + 2.

A) 2 a + h
B) 2 a + h $-$ 5
C) $-$ 2 a $-$ h + 5
D) a + h $-$ 2

Question 33

Specify the range for the following relation. Please enter your answer in interval notation. {( x , y ) | 5 x ² = 8 y ³}

Question 34

Specify the domain for the function. Please enter your answer in interval notation.

Question 35

Suppose that the cost function for producing a certain item is given by C ( n ) = 3 n + 4 where n represents the number of items produced. Find C (150), C (570), C (770), C (1,580).

A) C (150) = 474, C (570) = 1,734, C (770) = 2,334, C (1,580) = 4,764
B) C (150) = 464, C (570) = 1,724, C (770) = 2,324, C (1,580) = 4,754
C) C (150) = 484, C (570) = 1,744, C (770) = 2,344, C (1,580) = 4,774
D) C (150) = 454, C (570) = 1,714, C (770) = 2,314, C (1,580) = 4,744

Question 36

Specify the domain for the function. Please enter your answer in interval notation.

Question 37

Specify the domain for the function. Please enter your answer in interval notation.

Question 38

Specify the domain for the function. Please enter your answer in interval notation.

Question 39

Specify the domain for the function. Please enter your answer in interval notation.

Question 40

If $f ( x ) = \frac { 2 } { x - 5 }$ find $f ( - 5 ) , f ( 0 ) , f ( 5 ) , f ( - 3 )$ .

A) $f ( - 5 ) = - \frac { 1 } { 5 } , f ( 0 ) = - \frac { 2 } { 5 } , f ( 5 ) \text { does not exist, } f ( - 3 ) = - \frac { 1 } { 4 }$
B) $f ( - 5 ) \text { does not exist, } f ( 0 ) = - \frac { 2 } { 5 } , f ( 5 ) = \frac { 1 } { 5 } , f ( - 3 ) = - \frac { 1 } { 4 }$
C) $f ( - 5 ) = \frac { 1 } { 5 } , f ( 0 ) = - \frac { 2 } { 5 } , f ( 5 ) \text { does not exist, } f ( - 3 ) = - \frac { 1 } { 4 }$
D) $f ( - 5 ) = - \frac { 1 } { 5 } , f ( 0 ) = - \frac { 2 } { 5 } , f ( 5 ) = \frac { 1 } { 5 } , f ( - 3 ) = \frac { 1 } { 4 }$

Question 41

Identify the graph of the function. f ( x ) = -4 x ²

A)
B)
C)

Question 42

Identify the graph of the function. f ( x ) = $-$ 2 x 2 + 1

A)
B)
C)

Question 43

Identify the graph of the function. f ( x ) = $-$ 3 x 2 $-$ 8 x

A)
B)
C)

Question 44

Identify the graph of the function. f ( x ) = -5 x

A)
B)
C)

Question 45

Identify the graph of the function. f ( x ) = 3

A)
B)
C)

Question 46

The graph of a linear function of the form $f ( x ) = b$ is a vertical line.

Question 47

Identify the graph of the function. f ( x ) = 2 x $-$ 1

A)
B)
C)

Question 48

Find the vertex of $f ( x ) = 2 x ^ { 2 } - 3 x - 4$ .

A) $\left( \frac { 3 } { 4 } , - \frac { 41 } { 8 } \right)$
B) $\left( - \frac { 3 } { 4 } , - \frac { 5 } { 8 } \right)$
C) $\left( \frac { 3 } { 4 } , - \frac { 5 } { 8 } \right)$
D) $\left( - \frac { 3 } { 4 } , \frac { 41 } { 8 } \right)$

Question 49

Identify the graph of the function. f ( x ) = 3 x $-$ 5

A)
B)
C)

Question 50

Identify the graph of the function. f ( x ) = x ² + 4 x + 3

A)
B)
C)

Question 51

The graph of a quadratic equation is a parabola.

Question 52

Identify the graph of the function. f ( x ) = x 2 $-$ 3 x $-$ 1

A)
B)
C)

Question 53

Suppose that the profit function for selling n items is given by where n represents the number of items produced. Find .

Question 54

Identify the graph of the function. f ( x ) = $-$ ( x $-$ 1) 2 + 1

A)
B)
C)

Question 55

Find the x intercepts of $f ( x ) = 2 x ^ { 2 } - 11 x - 21$ .

A) $- \frac { 3 } { 2 }$ and 7
B) $- 21$
C) $- \frac { 3 } { 2 }$ and $- 7$
D) $- \frac { 2 } { 3 }$ and 7

Question 56

Identify the graph of the function. f ( x ) = $-$ 4 x 2 $-$ 19 x $-$ 21

A)
B)
C)

Question 57

Find for f ( x ) = x 2 8 x + 2.

Question 58

The function $f ( x ) = 2 x + 5$ is a linear function.

Question 59

Find for f ( x ) = x 2 6.

Question 60

The axis of symmetry for a parabola passes through the center of the parabola.

Question 61

Find the vertex of .

Question 62

Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $110.00 for 300 miles. On another day she rented a car from the same agency and paid $185.00 for 550 miles. Determine the linear function that the agency could use to determine its daily rental charges. Please enter your answer in the form f ( x ) = ax + b .

Question 63

The height of a projectile fired vertically into the air (neglecting air resistance) at an initial velocity of 144 feet per second is a function of the time and is given by the equation f ( x ) = 144 x $-$ 16 x 2 , where x represents the time. Find the highest point reached by the projectile.

A) 144 feet
B) 324 feet
C) 648 feet

Question 64

A motel advertises that it will provide dinner, a dance, and drinks at $30 per couple for a New Year's Eve party. It must have a guarantee of 60 couples. Furthermore, it will agree that for each couple in excess of 60, it will reduce the price per couple for all attending by $0.50. How many couples will it take to maximize the motel's revenue?

A) 120 couples
B) 60 couples
C) 0 couples

Question 65

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $22,500 and it depreciates $1,450 each year for t years. Find the value of the machinery after 8 years.

A) $11,600
B) $34,100
C) $10,900

Question 66

Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $60.00 for 200 miles. On another day she rented a car from the same agency and paid $90.00 for 350 miles. Determine the linear function that the agency could use to determine its daily rental charges.

A) f ( x ) = 0.2 x + 20
B) f ( x ) = $-$ 0.2 x + 20
C) f ( x ) = 0.2 x $-$ 20

Question 67

Find the x intercepts of .

Question 68

Three hundred meters of fencing is available to enclose a rectangular playground. What should be the dimensions of the playground to maximize the area?

Question 69

Suppose that the equation p ( x ) = 2 x 2 + 280 x 2,540, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit? __________ items

Question 70

Find two numbers whose sum is 48 and whose product is a maximum.

A) 24 and 24
B) 6 and 30
C) 36 and 12

Question 71

Suppose that the equation p ( x ) = $-$ 5 x 2 + 600 x $-$ 4,705, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit?

A) 600 items
B) 40 items
C) 60 items

Question 72

Find two numbers whose sum is 60 and whose product is a maximum. Please enter your answer as two numbers separated by a comma, without the units.

Question 73

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $25,500 and it depreciates $1,750 each year for t years. Set up a linear function that yields the value of the machinery after t years. Please enter your answer in the form f ( t ) = at + b .

Question 74

Zack wants to sell five items that cost him $1.50, $2.70, $5.20, $13.00, and $17.70. He wants to make a profit of 70% of the cost. Create a function that you can use to determine the selling price of each item, and then use the function to calculate each selling price.

A) Item 1 Item 2 Item 3 Item 4 Item 5 Cost $1.50 $2.70 $5.20 $13.00 $17.70 Selling price $4.05 $7.29 $14.04 $35.10 $47.79
B) Item 1 Item 2 Item 3 Item 4 Item 5 Cost $1.50 $2.70 $5.20 $13.00 $17.70 Selling price $2.55 $4.59 $8.84 $22.10 $30.09
C) Item 1 Item 2 Item 3 Item 4 Item 5 Cost $1.50 $2.70 $5.20 $13.00 $17.70 Selling price $1.05 $1.89 $3.64 $9.10 $12.39

Question 75

The height of a projectile fired vertically into the air (neglecting air resistance) at an initial velocity of 64 feet per second is a function of the time and is given by the equation f ( x ) = 64 x 16 x 2 , where x represents the time. Find the highest point reached by the projectile. __________ feet

Question 76

A motel advertises that it will provide dinner, a dance, and drinks at $40 per couple for a New Year's Eve party. It must have a guarantee of 60 couples. Furthermore, it will agree that for each couple in excess of 60, it will reduce the price per couple for all attending by $0.10. How many couples will it take to maximize the motel's revenue? __________ couples

Question 77

The cost for burning a 75-watt bulb is given by the function c ( h ) = 0.0045 h , where h represents the number of hours that the bulb burns. How much does it cost to burn a 75-watt bulb for 3 hours per night for a 31-day month? Express your answer to the nearest cent.

A) $0.50
B) $0.42
C) $0.33

Question 78

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $46,000 and it depreciates $850 each year for t years. Find the value of the machinery after 4 years. $ __________

Question 79

The cost for burning a 75-watt bulb is given by the function c ( h ) = 0.0045 h , where h represents the number of hours that the bulb burns. How much does it cost to burn a 75-watt bulb for 4 hours per night for a 30-day month? Express your answer to the nearest cent. $ __________

Question 80

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $32,000 and it depreciates $1,650 each year for t years. Set up a linear function that yields the value of the machinery after t years.

A) f ( t ) = 32,000 $-$ 1,650 t
B) f ( t ) = 1,650 t + 32,000
C) f ( t ) = 1,650 t $-$ 32,000