Deck 1: Functions and Their Graphs

Question 1

Determine if the relationship f = {(10, 1), (-15, -9), (-17, -9), (17, -4)} is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Answer 1

a function, but not one-to-one

Question 2

Determine if the relationship f = {(-12, -19), (20, 8), (7, 1), (-8, 9)} is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Answer 2

a one-to-one function

Question 3

Determine if the relationship f = {(20, -2), (20, -14), (4, -14), (-16, -6)} is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Answer 3

not a function

Question 4

Determine if the relationship is a function. If it is a function, determine if it is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 5

Determine if the relationship x = (y - 20)² + 18 is a function. If it is a function, determine if it is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 6

Determine if the relationship y = 5x¹¹ is a function. If it is a function, determine if it is one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 7

Determine if the relationship
, x > 0 is a function. If it is a function, determine if it is one-to-one.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 8

The function y = 7 - 6x is a one-to-one function. Find its inverse.

A)
B)
C)
D)

Question 9

The function f(x) = x² + 3, x $\ge$ 0 is a one-to-one function. Find its inverse.

A) y = x + 3
B)
C)
D)

Question 10

The function f(x) = (x - 3)² + 9, x $\ge$ 3 is a one-to-one function. Find its inverse.

A)
B)
C)
D)

Question 11

The function f(x) =

,

Is a one-to-one function. Find its inverse.

A)
B)
C)
D)

Question 12

The function

,

Is a one-to-one function. Find its inverse.

A)
B) y = 7
C)
D)

Question 13

The function

,

Is a one-to-one function. Find its inverse.

A)
B) y = -5
C)
D)

Question 14

Determine if the relationship

,

is a function. If it is, determine if it is a one-to-one function.

Question 15

The function

,

is a one-to-one function. Find its inverse.

Question 16

Determine whether the function is a one-to-one function.

Question 17

Determine whether the function is a one-to-one function.

A) a one-to-one function
B) not a one-to-one function

Question 18

Given the graph of a one-to-one function: plot its inverse.

Question 19

Given the graph of a one-to-one function: plot its inverse.

A)
B)
C)
D)

Question 20

Given the graph of a one-to-one function: plot its inverse.

Question 21

Given the graph of a one-to-one function: plot its inverse.

A)
B)
C)
D)

Question 22

A student work at Target making $8.3 per hour and the weekly number of hours worked per week, x, varies. If Target withholds 21% of his earnings for taxes and Social Security, write a function, E(x), that expresses the student's take-home pay each week. Find the inverse function, E ^-1(x). What does the inverse function tell you?

Question 23

A drug store pays you $9 per hour for the first 40 hours per week and time and a half for overtime. Write a piece-wise-defined function that represents your weekly earnings E(x) as a function of the number of hours worked, x. Find the inverse function

. What does the inverse function tell you?

Question 24

Verify that the function

is the inverse of

Question 25

Verify that the function

is the inverse of

Question 26

Verify that the function

is the inverse of

Question 27

Verify that the function

is the inverse of

Question 28

Verify that the function

is the inverse of

Question 29

Given the graph of the one-to-one function

Question 30

Given the graph of the one-to-one function

Question 31

Given the functions f(x) = 2x + 2 and g(x) = -9x + 6, find (f + g)(x).

A) -7x + 8
B) -7x + 4
C) 11x + 8
D) -18x + 12

Question 32

Given the functions f(x) = 13x² + 3 and g(x) = -9x² - 13, find (f + g)(x)

A) 4x² - 10
B) -4x² - 10
C) 4x² + 10
D) -4x² + 10

Question 33

Given the functions

And, find (f + g)(x)

A)
B)
C)
D)

Question 34

Given the functions f(x) = 17 - 9x and g(x) = 4x + 3, find (f - g)(x)

A) -13x + 14
B) -13x - 14
C) -13x + 20
D) 13x + 20

Question 35

Given the functions f(x) = 5x² + 6x and g(x) = -11x² + 11x, find (f - g)(x)

A) 16x² + 5x
B) 16x² - 5x
C) -6x² - 17x
D) -6x² - 5x

Question 36

Given the functions f(x) = x + 8 and g(x) = 3x - 6, find (f * g)(x)

A) 3x² + 48
B) 3x² + 18x - 48
C) 3x² + 24x + 48
D) 3x² - 48

Question 37

Given the equations f(x) = 5x² + 4 and g(x) = 4x² - 10, find (f * g)(x)

A) 20x⁴ - 40
B) 20x⁴ - 34x² - 40
C) 20x⁴ + 66x² - 40
D) 20x⁴ + 40

Question 38

Given the functions f(x) = 48x + 64 and g(x) = 6x + 8, find

A) 288x² + 768x + 512
B) 1/8
C) 8
D) 54x + 72

Question 39

Given the functions f(x) = x² - 9 and g(x) = x - 3, find

A) x + 3
B) x - 3
C) x² - x - 6
D) x + 9

Question 40

Given the equations f(x) = 10x + 4 and g(x) = 10x - 10, find

A) 20x - 6
B) 100x - 100
C) 100x - 96
D) 100x + 100

Question 41

Given the functions

And

, find

A)
B)
C)
D)

Question 42

Given the functions f(x) = 10x + 2 and g(x) = 2x - 9, find
.

A) 20x - 18
B) 20x - 7
C) 20x + 29
D) 20x - 5

Question 43

Given the functions f(x) =
and g(x) = 10 - x, find

.

A)
B) 10 -
C)
D)

Question 44

Given the functions f(x) = 2x² - 3 and g(x) = 3 - 3x, find
.

A) 69
B) -75
C) -18x² - 27
D) 285

Question 45

Given the function
and g(x) = |x|, find

A) -45 / 4
B) 45 / 4
C)
D)

Question 46

Given the functions f(x) = 9x - 3 and g(x) = 3x + 2, determine f + g, f - g, fg, and

.

Question 47

Given the functions

and

, determine the composite functions

and

.

Question 48

Given the functions f(x) = 7x² - 4x, and g(x) = -6 - x, find

and

Question 49

Typical supply and demand relationships state that as the number of units for sale increases, the market price decreases. Assume that the market price, p, and the number of units for sale, x, are related by the demand equation:
Assume that the cost, C(x), of producing x items is governed by the equation
and the revenue, R(x), generated by selling x units is governed by
a. Write the cost as a function of price p.
b. Write the revenue as a function of price p.
c. Write the profit as a function of price p.

Question 50

Given the functions

, and

, find

and

Question 51

Given the functions

, and

, find

And

A)
B)
C)
D)

Question 52

Assume that the market price p and the number of units for sale x are related by the demand equation:
Assume that the cost C(x) of producing x items is governed by the equation
and the revenue R(x) generated by selling x units is governed by
a. Write the cost as a function of price p.
b. Write the revenue as a function of price p.
c. Write the profit as a function of price p.

Question 53

Given the equations f(x) = 5x + 3 and g(x) = 5x - 9, find the domain of

Question 54

Given the equations f(x) =

and g(x) = 10x - 6, find the domain of

Question 55

Given the equations f(x) =

and g(x) = 7x - 4, find the domain of

Question 56

The graph of y = |x| shifted down 10 and to the right 11. Write the resulting function.

A) y = |x + 11| - 10
B) y = |x - 11| - 10
C) y = |x + 11| + 10
D) y = |x - 11| + 10

Question 57

The graph of y = |x| shifted up 11 and to the left 1. Write the resulting function.

A) y = |x + 1| + 11
B) y = |x - 1| - 11
C) y = |x - 11| - 1
D) y = |x + 11| + 1

Question 58

The graph of y = x² is shifted up 9 and to the left 1. Write the resulting function.

A) y = (x - 1)² - 9
B) y = (x - 9)² - 1
C) y = (x + 9)² + 1
D) y = (x + 1)² + 9

Question 59

The graph of y = x² is reflected about the x-axis and shifted to the right 9. Write the resulting function.

A) y = -(x - 9)²
B) y = -(x + 9)²
C) y = (x - 9)²
D) y = (-x - 9)²

Question 60

The graph of y = |x| is reflected about the x-axis and shifted up 7. Write the resulting function.

A) y = |x| + 7
B) y = -|x + 7|
C) y = -|x| + 7
D) y = -|x - 7|

Question 61

The graph of y = x³ is expanded by a factor of 9. Write the resulting function.

A) y = 9x³
B) y = x³ - 9
C) y = x³ + 9
D)

Question 62

The graph of y = x³ is contracted by a factor of 7. Write the resulting function.

A) y = 7x³
B) y = x³ - 7
C) y = x³ + 7
D)

Question 63

The graph of y = x⁴ is contracted by a factor of 3. Write the resulting function.

A) y = 3x⁴
B) y = x⁴ - 3
C) y = x⁴ + 3
D)

Question 64

The graph of y = x⁴ is expanded by a factor of 9. Write the resulting function.

A) y = 9x⁴
B) y = x⁴ - 9
C) y = x⁴ + 9
D)

Question 65

The graph of

Is reflected about the x-axis and shifted to the left 8. Write the resulting function.

A)
B)
C)
D)

Question 66

The graph of

Is reflected about the x-axis and shifted to the right 14 and up 7. Write the resulting function.

A)
B)
C)
D)

Question 67

Write the function that results from shifting y = x² + 3 to the left 2 and reflecting about the x-axis.

A) y = -(x + 2)² - 3
B) y = -(x - 2)² - 3
C) y = -(x + 2)² + 3
D) y = -(x - 2)² + 3

Question 68

Write the function that results from shifting

To the right 8 and up 7.

A)
B)
C)
D)

Question 69

Write the function resulting from shifting f(x) = 8x² + 4 to the left 5 and up 10.

A) y = 8(x + 5)² + 14
B) y = 8(x + 5)² + 10
C) y = 8(x - 5)² + 10
D) y = 8(x - 5)² + 14

Question 70

The graph of y = x² is expanded by a factor of 4, shifted to the left 16, and up 13. Write the resulting function.

Question 71

The graph of y = |x| + 10 is expanded by a factor of 9 and reflected about the x-axis. Write the resulting function.

Question 72

Transform the function f(x) =

to the form f(x) = c(x - h)² + k, where c, h, and k are constants, by completing the square.

Question 73

For the given graph of a function f(x) draw the indicated function.
y = f(x - 3) - 1

Question 74

For the given graph of a function f(x) draw the indicated function.
y = f(x + 4) - 4

Question 75

For the given graph of a function f(x) draw the indicated function.
y = -2f(x - 3) + 2

Question 76

For the given graph of a function f(x) draw the indicated function.
y = -f(x) + 1

Question 77

For the given graph of a function f(x) draw the indicated function.

Question 78

For the given graph of a function f(x) draw the indicated function.

Question 79

For the given graph of a function f(x) draw the indicated function.
y = f(2x)

Question 80

For the given graph of a function f(x) draw the indicated function.
y = f(x + 1) - 1