Deck 9: Functions

Question 1

The distance that a freely falling body falls varies directly as the square of the time it falls. If a body falls 640 feet in 8 seconds, how far will it fall in 13 seconds?

A)d = 1,699 feet
B)d = 1,705 feet
C)d = 1,690 feet
D)d = 1,677 feet
E)d = 1,717 feet

Answer 1

d = 1,690 feet

Question 2

Determine whether the linear equation defines $y$ to be a function of $x$ . If so, find the domain and range. $y = \frac { 1 } { 3 } x - 1$

A)domain: $( - \infty , 0 )$ ; range: $( 0 , \infty )$
B)domain: $( 0 , \infty )$ ; range: $( - \infty , \infty )$
C)domain: $( - \infty , \infty )$ ; range: $( - \infty , \infty )$
D)domain: $( - \infty , \infty )$ ; range: $( 0 , \infty )$
E) $y$ is not a function of $x$

Answer 2

domain: $( - \infty , \infty )$ ; range: $( - \infty , \infty )$

Question 3

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x )= x 2 - 8 x + 2.

A)2 a + h
B)a + h - 2
C)-2 a - h + 8
D)2 a + h - 10
E)2 a + h - 8

Answer 3

2 a + h - 8

Question 4

Tell whether the equation determines y to be a function of x . $y ^ { 2 } = x + 7$

A)no
B)yes

Question 5

The volume of a cylinder varies jointly as its altitude and the square of the radius of its base. If the volume of a cylinder is 2,199 cubic centimeters when the radius of the base is 10 centimeters and its altitude is 7 centimeters, find the volume of a cylinder that has a base of radius 70 centimeters. The altitude of the cylinder is 56 centimeters.

A)V = 861,952 cm ³
B)V = 862,023 cm ³
C)V = 861,979 cm ³
D)V = 862,008 cm ³
E)V = 862,118 cm ³

Question 6

If you have the following function, f ( x )= -7| x | + 8, compute f (1), f (-3), f (2), f (-4)

A)f (1)= 1, f (-3)= -13, f (2)= -6, f (-4)= -20
B)f (1)= 2, f (-3)= -14, f (2)= -5, f (-4)= -21
C)f (1)= 2, f (-3)= -11, f (2)= -7, f (-4)= -18
D)f (1)= 4, f (-3)= -15, f (2)= -3, f (-4)= -22
E)f (1)= -1, f (-3)= 13, f (2)= 6, f (-4)= 20

Question 7

Tell whether the equation determines y to be a function of x . y = 3.2 x + 8

A)no
B)yes

Question 8

Graph the linear function. f ( x )= 3 x + 9

A)
B)
C)
D)

Question 9

Identify the graph of the function. f ( x )= x ² + 6 x + 5

A)
B)
C)
D)
E)

Question 10

If you have the following function f ( x )= 9 x + 7, compute f (1), f (-3), f (4), f (-6).

A)f (1)= 19, f (-3)= -22, f (4)= 46, f (-6)= -49
B)f (1)= 16, f (-3)= -20, f (4)= 43, f (-6)= -47
C)f (1)= 15, f (-3)= -19, f (4)= 42, f (-6)= -46
D)f (1)= 17, f (-3)= -21, f (4)= 44, f (-6)= -48
E)f (1)= -16, f (-3)= 20, f (4)= - 43, f (-6)= 47

Question 11

Graph the linear function. $$f ( x ) = - \frac { 3 } { 5 } x - 6$$

A)
B)
C)
D)

Question 12

Identify the graph of the function. f ( x )= -3 x ² - 6 x

A)
B)
C)
D)
E)

Question 13

If you have the following function, f ( x )= - x ² - 5 x + 4, compute f (3), f (-2), f (5), f (-4).

A)f (3)= 0, f (-2)= 21, f (5)= 6, f (-4)= 43
B)f (3)= -2, f (-2)= 18, f (5)= 4, f (-4)= 40
C)f (3)= 1, f (-2)= 20, f (5)= 7, f (-4)= 42
D)f (3)= -1, f (-2)= 19, f (5)= 5, f (-4)= 41
E)f (3)= -3, f (-2)= 16, f (5)= 2, f (-4)= 39

Question 14

The time required for a car to travel a certain distance varies inversely as the rate at which it travels. If it takes 10 hours at 60 miles per hour to travel the distance, how long will it take at 100 miles per hour?

A)t = 6 hours
B)t = 10 hours
C)t = 5 hours
D)t = 9 hours
E)t = 4 hours

Question 15

Graph the linear function. f ( x )= - 2

A)
B)
C)
D)

Question 16

Determine both the domain and the range of the function. $$y = f ( x ) = - 2 | x |$$

A)Domain: the set of real numbers greater than or equal to 0. Range: the set of real numbers.
B)Domain: the set of real numbers. Range: the set of real numbers less than or equal to 0.
C)Domain: the set of real numbers less than or equal to 0. Range: the set of real numbers.
D)Domain: the set of real numbers. Range: the set of real numbers greater than or equal to 0.
E)Domain: the set of real numbers greater than or equal to 0. Range: the set of real numbers less than or equal to 0.

Question 17

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x )= - x 2 - 7.

A)h + a
B)-7
C)-2 a - h
D)7 a
E)-2 a ² - h

Question 18

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

A)
B)
C)
D)
E)

Question 19

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

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

Question 20

Tell whether the equation determines y to be a function of x . $y = 7 x ^ { 2 }$

A)no
B)yes

Question 21

Graph the function $y = \sqrt { x }$ .

A)
B)
C)
D)

Question 22

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 5 x + 4$ and $g ( x ) = 3 x - 7$ .

A) $15 x$
B) $15 x ^ { 2 } + 5$
C) $15 x + 5$
D) $15 x - 5$
E) $15 - 7 x$

Question 23

Draw the graph using a translation of the graph of $f ( x ) = | x |$ . $f ( x ) = | x + 3 | + 4$

A)
B)
C)
D)
E)

Question 24

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 2 hours per night for a 31-day month? Express your answer to the nearest cent.

A)$0.28
B)$0.21
C)$0.27
D)$0.22
E)$0.33

Question 25

For the function, first sketch the graph of its associated function, $g ( x ) = x ^ { 3 }$ . Then draw the graph using a reflection. $f ( x ) = - x ^ { 3 }$

A)
B)
C)
D)
E)

Question 26

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $33,000 and it depreciates $850 each year for t years. Set up a linear function that yields the value of the machinery after t years.

A)f ( t )= 850 t - 33,000
B)f ( t )= 850 t + 33,000
C)f ( t )= 33,000 - 850 t
D)f ( t )= 33,000 t + 850
E)f ( t )= 33,000 t - 850

Question 27

Graph the function $y = \frac { 1 } { x }$ .

A)
B)
C)
D)

Question 28

Graph the function. Check your work with a graphing calculator. $f ( x ) = ( x + 3 ) ^ { 3 }$

A)
B)
C)
D)
E)

Question 29

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 9 x$ and $g ( x ) = 5 x - 5$ .

A) $45$
B) $$45 - 5 x$$
C) $45 x - 5$
D) $45 x ^ { 2 } - 5$
E) $45 x + 5$

Question 30

Draw the graph using a translation of the graph of $f ( x ) = x ^ { 3 }$ . $f ( x ) = ( x + 4 ) ^ { 3 } - 1$

A)
B)
C)
D)
E)

Question 31

Graph the function $y = - | x |$ .

A)
B)
C)
D)

Question 32

Graph the function. $f ( x ) = - 5 \sqrt { x }$

A)
B)
C)
D)

Question 33

Graph the function. $f ( x ) = \frac { 1 } { 6 } | x |$

A)
B)
C)
D)

Question 34

Graph the function $y = \sqrt { - x }$ .

A)
B)
C)
D)

Question 35

Graph the function. $f ( x ) = \frac { 1 } { 2 } x ^ { 2 }$

A)
B)
C)
D)

Question 36

Graph the function $y = x ^ { 3 }$ .

A)
B)
C)
D)

Question 37

Sketch the graph of the associated function, $g ( x ) = | x |$ then draw the graph of the function f using translation and/or a reflection. $f ( x ) = | x - 4 | - 1$

A)
B)
C)
D)
E)

Question 38

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 $100.00 for 300 miles. On another day she rented a car from the same agency and paid $150.00 for 550 miles. Determine the linear function that the agency could use to determine its daily rental charges.

A)f ( x )= 0.4 x - 40
B)f ( x )= 0.4 x + 40
C)f ( x )= -0.2 x + 40
D)f ( x )= 0.2 x - 40
E)f ( x )= 0.2 x + 40

Question 39

Graph the function. Check your work with a graphing calculator. $f ( x ) = | x | + 7$

A)
B)
C)
D)
E)

Question 40

Graph the function. Check your work with a graphing calculator. f ( x )= x ² + 5

A)
B)
C)
D)

Question 41

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 8 x + 3$ and $g ( x ) = x ^ { 2 } + 7$ .

A) $( 8 x + 3 ) ^ { 2 } + 7$
B) $( 8 x ) ^ { 2 } + 7$
C) $8 x + 10$
D) $( 3 x + 8 ) ^ { 2 } - 7$
E) $( 8 x - 3 ) ^ { 2 } - 7$

Question 42

Use the vertical line test to determinate if curve is a function.

A)yes
B)no

Question 43

Use the vertical line test to determinate if curve is a function.

Question 44

Find the constant of variation for the stated condition: y varies directly as x , and y = 150 when x = 240.

A) $k = \frac { 5 } { 4 }$
B) $k = \frac { 1 } { 4 }$
C) $k = 14,580$
D) $k = \frac { 4 } { 5 }$
E) $k = \frac { 1 } { 5 }$

Question 45

Form the inverse function of the function and list the range of the inverse function. f = { (1, 8), (2, 9), (4, 11), (3, 7)}

A){ 1, 8, 2, 9 }
B){ 1, 2, 4, 3 }
C){ 4, 9, 3, 7 }
D){ 0, 2, 4, 3 }
E){ 8, 9, 11, 7 }

Question 46

At a constant temperature, the volume ( V )of a gas varies inversely as the pressure ( P ). Translate the statement of variation into an equation and use k as the constant of variation.

A) $B = \frac { k } { H }$
B) $k = \frac { H } { B }$
C) $B = \frac { H } { k }$
D) $H = k b$
E) $H = \frac { k } { B }$

Question 47

Determine whether the function is one-to-one. $f ( x ) = x ^ { 4 }$

A)no
B)yes

Question 48

Form the inverse function of the function and list the domain of the inverse function. f = { (2, -6), (5, -8), (7, -2)}

A){ 2, -8, 7 }
B){ 2, 5, -2 }
C){ -6, 5, -2 }
D){ 2, 5, 7 }
E){ -6, -8, -2 }

Question 49

Tell whether the inverse of the set of ordered pairs $( x , y )$ is a function. $\{ ( 5,2 ) , ( 6,2 ) , ( 7,2 ) , ( 8,2 ) \}$

A)no
B)yes

Question 50

The volume ( B )of a gas varies directly as the absolute temperature ( T )and inversely as the pressure ( D ). Translate the statement of variation into an equation and use k as the constant of variation.

A) $B = k T D$
B) $B = \frac { T } { \mathrm { D } }$
C) $B = \frac { k D } { T }$
D) $B = \frac { k T } { D }$
E) $B = \frac { D } { T }$

Question 51

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 7 } { 4 x }$ and $g ( x ) = \frac { 1 } { x + 3 }$ .

A) $( - \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0 , \infty )$
B) $( - \infty , - 3 ) \cup ( - 3 , \infty )$
C) $( - \infty , - 3 ) \cup ( 0 , \infty )$
D) $\left( - \infty , - \frac { 7 } { 12 } \right) \cup \left( - \frac { 7 } { 12 } , 0 \right) \cup ( 0 , \infty )$
E) $( - \infty , 0 ) \cup ( 0 , \infty )$

Question 52

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 5 x + 6$ and $g ( x ) = x ^ { 2 } + 3$ .

A) $( - \infty , \infty )$
B) $( - \infty , 0 ] \cup [ 0 , \infty )$ $( - \infty , 0 ) \cup ( 0 , \infty )$
C) $( - \infty , 0 )$
D) $( - \infty , 0 ) \cup ( 0 , \infty )$
E) $( 0 , \infty )$

Question 53

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = 3 x$ and $g ( x ) = 8 x - 7$ .

A) $( - \infty , 0 )$
B) $( - \infty , 0 ) \cup ( 0 , \infty )$
C) $( 0 , \infty )$
D) $( - \infty , \infty )$
E) $( - \infty , 0 ]$

Question 54

Translate the statement of variation into an equation and use k as the constant of variation. d varies directly as the cube of t .

A)t = kd ³
B)d = t ³
C) $d = \frac { k } { b ^ { 3 } }$
D)d = kt ³
E)d = kt

Question 55

True or false? The function below is one-to-one function. f ( x )= - x ⁸

Question 56

Find the inverse of the given function and express it in the form $y = f ^ { - 1 } ( x )$ . Verify the result by showing that $\left( f \circ f ^ { - 1 } \right) ( x ) = \left( f ^ { - 1 } \circ f \right) ( x ) = I ( x )$ . $f ( x ) = \frac { 2 x + 10 } { 5 }$

A) $f ^ { - 1 } ( x ) = 5 x - 2$
B) $f ^ { - 1 } ( x ) = \frac { 5 } { 2 } x - 5$
C) $f ^ { - 1 } ( x ) = \frac { 2 } { 5 } x + 2$
D) $f ^ { - 1 } ( x ) = \frac { 5 } { 2 } x + 5$
E) $f ^ { - 1 } ( x ) = 2 x + 5$

Question 57

Find the inverse of the given function and express it in the form $y = f ^ { - 1 } ( x )$ . Verify the result by showing that $\left( f \circ f ^ { - 1 } \right) ( x ) = \left( f ^ { - 1 } \circ f \right) ( x ) = I ( x )$ . $x + 4 = 9 y$

A) $f ^ { - 1 } ( x ) = 4 x + 9$
B) $f ^ { - 1 } ( x ) = 9 x - 4$
C) $$f ^ { - 1 } ( x ) = 4 x - 9$$
D) $f ^ { - 1 } ( x ) = 9 x + 4$
E) $f ^ { - 1 } ( x ) = 9 ( x - 4 )$

Question 58

Translate the statement of variation into an equation and use k as the constant of variation. A varies jointly as n and t .

A)A = knt
B)n = kAt
C) $C = \frac { k t } { m }$
D)A = nt
E) $C = \frac { k } { m t }$

Question 59

Determine whether the function is one-to-one. $$f ( x ) = x ^ { 8 } + 8$$

A)yes
B)no

Question 60

Find the inverse of the function and express it using $f ^ { - 1 } ( x )$ notation. $f ( x ) = 4 x ^ { 3 } - 2$

A) $f ^ { - 1 } ( x ) = \sqrt { \frac { x + 2 } { 4 } }$
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 4 } { 2 } }$
C) $f ^ { - 1 } ( x ) = \left( \frac { x + 2 } { 4 } \right) ^ { 3 }$
D) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 2 } { 4 } }$
E) $f ^ { - 1 } ( x ) = \left( \frac { x + 4 } { 2 } \right) ^ { 3 }$

Question 61

Find the constant of variation for the stated condition: y varies inversely as x , and y = -144 when $x = \frac { 8 } { 7 }$ .

A) $k = - \frac { 7 } { 8 }$
B) $k = - 35 \frac { 8 } { 7 }$
C)k = 156
D) $k = - \frac { 8 } { 7 }$
E)k = -156

Question 62

Find the constant of variation for the stated condition: y varies directly as x and inversely as z , and y = 185 when x = 70 and z = 14.

A)k = 37
B)k = 12,950
C)k = 5
D) $k = \frac { 1 } { 189 }$
E) $k = \frac { 1 } { 9 }$

Question 63

Find the constant of variation for the stated condition: A varies jointly as b and h , and A = 48 when b = 64 and h = 2.

A) $k = 3$
B) $k = 5$
C) $k = - \frac { 4 } { 3 }$
D) $k = \frac { 3 } { 4 }$
E) $k = \frac { 4 } { 3 }$