Deck 3: Functions and Their Graphs

Question 1

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Answer 1

not a function

Question 2

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Answer 2

function

Question 3

Determine whether the relation represents a function. If it is a function, state the domain and range.
{(-3, 6), (1, 4), (4, -4), (7, -1)}

A)function domain: {-3, 1, 4, 7}
Range: {6, 4, -4, -1}
B)function domain: {6, 4, -4, -1}
Range: {-3, 1, 4, 7}
C)not a function

Answer 3

function domain: {-3, 1, 4, 7}
Range: {6, 4, -4, -1}

Question 4

Determine whether the relation represents a function. If it is a function, state the domain and range.
{(-1, -3), (-2, -2), (-2, 0), (2, 2)

A)function domain: {-1, 2, -2, 14}
Range: {-3, -2, 0, 2, 4}
, (14, 4)}
B)function domain: {-3, -2, 0, 2, 4}
Range: {-1, 2, -2, 14}
C)not a function

Question 5

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Question 6

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Question 7

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Question 8

Determine whether the relation represents a function. If it is a function, state the domain and range.

A)function domain: {5, 10, 15, 20}
Range: {30, 60, 90, 120}
B)function domain:{30, 60, 90, 120}
Range: {5, 10, 15, 20}
C)not a function

Question 9

Find the value for the function.
Find f(-3)when f(x)=

A)-11
B)-1
C)29
D)19

Question 10

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Question 11

Find the value for the function.
Find f(2)when f(x)=

A)
B)2
C)
D)4

Question 12

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Question 13

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Question 14

Determine whether the equation defines y as a function of x.
y =

A)function
B)not a function

Question 15

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Question 16

Determine whether the relation represents a function. If it is a function, state the domain and range.

A)function domain: {Alice, Brad, Carl}
Range: {snake, cat, dog}
B)function domain: {snake, cat, dog}
Range: {Alice, Brad, Carl}

Question 17

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Question 18

Determine whether the relation represents a function. If it is a function, state the domain and range.
{(-4, 20), (-3, 13), (0, 4), (3, 13),

A)function domain: {-4, -3, 0, 3, 5}
Range: {20, 13, 4, 29}
(5, 29)}
B)function domain: {20, 13, 4, 29}
Range: {-4, -3, 0, 3, 5}
C)not a function

Question 19

Determine whether the relation represents a function. If it is a function, state the domain and range.
{(2.11, 9.21), (2.111, -9.2),

A)function domain:
Range: {9.21, -9.2, 0, -2}
B)function domain: {9.21, -9.2, 0, -2}
Range:
C)not a function

Question 20

Determine whether the equation defines y as a function of x.

A)function
B)not a function

Question 21

Find the value for the function.
Find f(2x)when f(x)= .

A)
B)
C)
D)

Question 22

Find the value for the function.
Find -f(x)when f(x)=

A)
B)
C)
D)

Question 23

Find the value for the function.
Find f(x + h)when

A)
B)
C)2
D)

Question 24

Find the value for the function.
Find f(4)when f(x)=

A)
B)5
C)
D)

Question 25

Find the value for the function.
Find f(-x)when f(x)=

A)
B)
C)
D)

Question 26

Solve the problem.
If f(x)= and f(-7)is undefined, what are the values of A and B?

A)A = -7, B = -1
B)A = -1, B = -7
C)A = 7, B = 1
D)A = 1, B = 7

Question 27

Solve the problem.
The function F described by F(C)= gives the Fahrenheit temperature corresponding to the Celsiustemperature C. Find the Fahrenheit temperature equivalent to -5°C.

A)23°F
B)14°F
C)5°F
D)-4°F

Question 28

Find the value for the function.
Find f(-9)when f(x)=

A)3
B)-15
C)15
D)-3

Question 29

Solve the problem.
If a rock falls from a height of 30 meters on Earth, the height H (in meters)after x seconds is approximately What is the height of the rock when x = 1.7 seconds? Round to the nearest hundredth, if necessary.

A)15.84 m
B)44.16 m
C)21.67 m
D)16.13 m

Question 30

Solve the problem.
The function gives the pressure, in atmospheres (atm), at a depth d feet in the sea. Find thepressure at 39 feet.

A) atm
B) atm
C) atm
D) atm

Question 31

Solve the problem.
It has been determined that the number of fish f(t)that can be caught in t minutes in a certain pond using acertain bait is Find the approximate number of fish that can be caught if you fishfor 30 minutes.

A)About 9 fish
B)About 20 fish
C)About 32 fish
D)About 34 fish

Question 32

Find the value for the function.
Find f(x - 1)when f(x)=

A)
B)
C)
D)

Question 33

Find the value for the function.
Find f(-x)when f(x)=

A)
B)
C)
D)

Question 34

Find the value for the function.
Find f(-x)when f(x)=

A)
B)
C)
D)

Question 35

Solve the problem.
If f(x)= nd f(-5)= -10, what is the value of A?

A)A = 53
B)A = -53
C)A = -28
D)A = 28

Question 36

Find the value for the function.
Find -f(x)when f(x)=

A)
B)
C)
D)

Question 37

Find the value for the function.
Find f(x + h)when f(x)=

A)
B)
C)
D)

Question 38

Solve the problem.
If a rock falls from a height of 60 meters on Earth, the height H (in meters)after x seconds is approximately When does the rock strike the ground? Round to the nearest hundredth, if necessary.

A)3.5 sec
B)12.24 sec
C)1.58 sec
D)2.5 sec

Question 39

Find the value for the function.
Find f(x + 1)when f(x)=

A)
B)
C)
D)

Question 40

Solve the problem.
If f(x)= C and f(3)= 1, what is the value of C?

A)C = -131
B)C = 25
C)C = 31
D)C = 139

Question 41

Find the domain of the function.

A)all real numbers
B)
C)
D)

Question 42

For the given functions f and g, find the requested function and state its domain.
f(x)= 4x - 9; g(x)= 6x - 2Find f - g.

A)(f - g)(x)= -2x - 7; all real numbers
B)
C)
D)(f - g)(x)= 2x + 7; all real numbers

Question 43

Find the domain of the function.

A)
B)
C)
D)all real numbers

Question 44

For the given functions f and g, find the requested function and state its domain.
f(x)= Find f ∙ g.

A)(f ∙ g)(x)=
B)(f ∙ g)(x)=
C)(f ∙ g)(x)=
D)(f ∙ g)(x)=

Question 45

For the given functions f and g, find the requested function and state its domain.
f(x)= Find f ∙ g.

A)
B)
C)
D)

Question 46

For the given functions f and g, find the requested function and state its domain.
f(x)= Find f + g.

A)(f + g)(x)= - - x + 20; all real numbers
B)(f + g)(x)= 4 + x; {x|x 4}
C)(f + g)(x)= - all real numbers
D)(f + g)(x)= all real numbers

Question 47

For the given functions f and g, find the requested function and state its domain.
f(x)= Find f ∙ g.

A) all real numbers
B) all real numbers
C)(
D) all real numbers

Question 48

Find the domain of the function.

A)all real numbers
B)
C)
D)

Question 49

For the given functions f and g, find the requested function and state its domain.
f(x)= Find f + g.

A)
B)
C)(
D)

Question 50

For the given functions f and g, find the requested function and state its domain.
f(x)= 6x - 4; g(x)= 5x + 2Find f ∙ g.

A) all real numbers
B)
C) all real numbers
D)

Question 51

For the given functions f and g, find the requested function and state its domain.
Find

A)
B)
C)
D)

Question 52

For the given functions f and g, find the requested function and state its domain.
f(x)= Find .

A)
B)
C)
D)

Question 53

Find the domain of the function.

A)
B)
C)
D)all real numbers

Question 54

For the given functions f and g, find the requested function and state its domain.
f(x)= x + 5; g(x)= Find f - g.

A)(f - g)(x)= all real numbers
B) all real numbers
C)
D) all real numbers

Question 55

Find the domain of the function.
f(x)= 2x + 3

A)all real numbers
B)
C)
D)

Question 56

Find the domain of the function.

A)
B)
C)
D)all real numbers

Question 57

Solve the problem.
Given f(x)= find the function g.

A)
B)
C)
D)

Question 58

For the given functions f and g, find the requested function and state its domain.
f(x)= 2 - 3x; g(x)= -7x + 3Find f + g.

A)(f + g)(x)= -10x + 5; all real numbers
B)
C)(f + g)(x)= -5x; all real numbers
D)

Question 59

Solve the problem.
Find (f + g)(-4)when f(x)= x - 2 and g(x)= x + 1.

A)-9
B)-5
C)-11
D)-7

Question 60

Find the domain of the function.

A)
B)
C)
D)

Question 61

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts,
if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

A)function domain:
Range:
Intercepts: (-4, 0), (0, -4), (0, 4), (4, 0)symmetry: x-axis, y-axis, origin
B)function domain:
Range:
Intercepts: (-4, 0), (0, -4), (0, 4), (4, 0)symmetry: x-axis, y-axis
C)function domain:
Range:
Intercepts: (-4, 0), (0, -4), (0, 0), (0, 4), (4, 0)symmetry: origin
D)not a function

Question 62

Solve the problem.
A retail store buys 35 VCRs from a distributor at a cost of $150 each plus an overhead charge of $30 perorder. The retail markup is 30% on the total price paid. Find the profit on the sale of one VCR.

A)$45.26
B)$4,526.00
C)$45.00
D)$44.74

Question 63

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts,
if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

A)function domain: all real numbers
Range:
Intercepts: (-3, 0), (0, 3), (1, 0)symmetry: none
B)function domain:
Range: all real numbers
Intercepts: (-3, 0), (0, 3), (1, 0)symmetry: y-axis
C)function domain: all real numbers
Range:
Intercepts: (0, -3), (3, 0), (0, 1)symmetry: none
D)not a function

Question 64

Solve the problem.
Express the gross salary G of a person who earns $40 per hour as a function of the number x of hoursworked.

A)G(x)= 40x
B)G(x)= 40 + x
C)
D)

Question 65

Find and simplify the difference quotient of f, for the function.

A)
B)
C)
D)0

Question 66

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts,
if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

A)function domain:
Range: {
Intercepts:
Symmetry: origin
B)function domain:
Range:
Intercepts:
Symmetry: none
C)function domain: all real numbers
Range:
Intercepts:
Symmetry: origin
D)not a function

Question 67

Find and simplify the difference quotient of f, for the function.

A)2x+ h + 6
B)
C)2x+ h - 9
D)1

Question 68

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts,
if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

A)function domain:
Range: all real numbers
Intercept: (1, 0)symmetry: none
B)function domain:
Range: all real numbers
Intercept: (0, 1)symmetry: origin
C)function domain: all real numbers
Range:
Intercept: (1, 0)symmetry: none
D)not a function

Question 69

Solve the problem.
Find (fg)(3)when f(x)= x - 7 and g(x)=

A)-4
B)-350
C)10
D)-184

Question 70

Find and simplify the difference quotient of f, for the function.
f(x)= 3x + 1

A)3
B)
C)
D)0

Question 71

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts,
if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

A)function domain:
Range: all real numbers
Intercepts: (-3, 0), (3, 0)symmetry: x-axis, y-axis, origin
B)function domain: all real numbers
Range:
Intercepts: (-3, 0), (3, 0)symmetry: y-axis
C)function domain:
Range: all real numbers
Intercepts: (-3, 0), (3, 0)symmetry: x-axis, y-axis
D)not a function

Question 72

Solve the problem.
Jacey, a commissioned salesperson, earns $420 base pay plus $49 per item sold. Express Jaceyʹs grosssalary G as a function of the number x of items sold.

A)G(x)= 49x + 420
B)G(x)= 420x +49
C)G(x)= 49(x + 420)
D)G(x)= 420(x + 49)

Question 73

Solve the problem.
Find (f - g)(5)when f(x)= - 1 and g(x)= x + 7.

A)87
B)
C)101
D)97

Question 74

Solve the problem.
The function f(t)= models the U.S. population in millions, ages 65 and older, where trepresents years after 1990. The function models the total yearly cost ofMedicare in billions of dollars, where t represents years after 1990. What does the function represent?Find

A)Cost per person in thousands of dollars. $11.54 thousand
B)Cost per person in thousands of dollars. $0.17 thousand
C)Cost per person in thousands of dollars. $0.09 thousand
D)Cost per person in thousands of dollars. $10.61 thousand

Question 75

Find and simplify the difference quotient of f, for the function.
f(x)= 4

A)0
B)1
C)
D)4

Question 76

Find and simplify the difference quotient of f, for the function.
f(x)=

A)4(2x+h)
B)
C)
D)4

Question 77

Solve the problem.
Find -5)when f(x)= 2x - 5 and g(x)=

A)
B)
C)1
D)0

Question 78

Solve the problem.
A firm is considering a new product. The accounting department estimates that the total cost, C(x), of produx units will beC(x)= 60x + 3,680.The sales department estimates that the revenue, R(x), from selling x units will beR(x)= 70x,but that no more than 485 units can be sold at that price. Find and interpret (R -C)(485).

A)$1,170 profit, income exceeds cost It is worth it to develop product.
B)-$1,170 loss, cost exceeds income It is not worth it to develop product.
C)$66,730 profit, income exceeds cost It is worth it to develop product.
D)$853 profit, income exceeds cost It is worth it to develop product.

Question 79

Solve the problem.
The following graph shows the private, public and total national school enrollment for students for selectyears from 1970 through 2000. i)How is the graph for total school enrollment, T, determined from the graph of the private enrollment, r,the public enrollment, u?ii)During which 10-year period did the total number of students enrolled increase the least?iii)During which 10-year period did the total number of students enrolled increase the most?

A)i)T is the sum of r and u. ii)1970 - 1980
Iii)1990-2000
B)i)T is the sum of r and u. ii)1990-2000
Iii)1970-1980
C)i)T is the sum of r and u. ii)1970 - 1980
Iii)1980-1990
D)i)T is the difference of r and u. ii)1970 - 1980
Iii)1990-2000

Question 80

Solve the problem.
Suppose that P(x)represents the percentage of income spent on housing in year x and I(x)representsincome in year x. Determine a function H that represents total housing expenditures in year x.

A)H(x)= (P ∙ I)(x)
B)H(x)= (P + I)(x)
C)H(x)= (I - P)(x)
D)