Deck 2: Functions and Graphs

Question 1

Determine whether the relation is a function.
{(-7, 7), (-7, 6), (1, -7), (5, 7), (8, 2)}

A) No
B) Yes

Answer 1

No

Question 2

Determine whether the relation is a function.
{(-6, 4), (-3, -9), (-1, 1), (4, -3)}

A) Yes
B) No

Answer 2

Yes

Question 3

For the given pair of variables determine whether a is a function of b, b is a function of a, both, or neither.
a is the savings account number of a customer at a bank, and b is the number of years the account has been active.

A) a is a function of b
B) Neither
C) Both
D) b is a function of a

Answer 3

b is a function of a

Question 4

Determine whether the relation is a function.
{(-8, 8), (-8, 9), (-1, 6), (6, -1), (8, -9)}

A) No
B) Yes

Question 5

Determine whether the relation is a function.
{(-1, -5), (2, 1), (5, -6), (7, 3), (10, 4)}

A) Yes
B) No

Question 6

Determine whether the relation is a function.
{(-5, 4), (-1, 3), (1, 4), (6, -5)}

A) No
B) Yes

Question 7

Determine whether the relation is a function.

A) No
B) Yes

Question 8

Determine whether the relation is a function.
{(-6, 7), (-3, -1), (3, 4), (3, -1)}

A) No
B) Yes

Question 9

Determine whether the relation is a function.
{(-6, 1), (-3, -1), (2, 5), (2, -3)}

A) No
B) Yes

Question 10

Use the vertical line test to determine whether y is a function of x.

A) No
B) Yes

Question 11

Determine whether the relation is a function.

A) No
B) Yes

Question 12

Determine whether the relation is a function.
{(3, 1), (3, 8), (4, 7), (8, -6), (11, -1)}

A) Yes
B) No

Question 13

Use the vertical line test to determine whether y is a function of x.

A) No
B) Yes

Question 14

Use the vertical line test to determine whether y is a function of x.

A) Yes
B) No

Question 15

For the given pair of variables determine whether a is a function of b, b is a function of a, both, or neither.
a is the radius of any spherical bowling ball, and b is its volume.

A) b is a function of a
B) Neither
C) a is a function of b
D) Both

Question 16

Use the vertical line test to determine whether y is a function of x.

A) Yes
B) No

Question 17

Use the vertical line test to determine whether y is a function of x.

A) Yes
B) No

Question 18

Use the vertical line test to determine whether y is a function of x.

A) Yes
B) No

Question 19

For the given pair of variables determine whether a is a function of b, b is a function of a, both, or neither.
a is the number of years of formal education of an adult living in the United States, and b is his or her age in years.

A) a is a function of b
B) Neither
C) Both
D) b is a function of a

Question 20

Use the vertical line test to determine whether y is a function of x.

A) No
B) Yes

Question 21

Find the domain and range.
{(2, 1), (6, 3), (-6, 6), (-6, 8)}

A) D = {2, 6, -6}; R = {1, 3, 6, 8}
B) D = {1, 3, 6, 8}; R = {2, 6, -6}
C) D = {2, 6, -6, -6}; R = {1, 3, 6, 8}
D) D = {2, 6, -6, 6}; R = {1, 3, 6, 8}

Question 22

Find the domain and range.
{(-5, -11), (-9, -10), (12, 7), (6, 2), (-3, 3)}

A) D = {-10, -11, 3, 7, 2}; R = {-9, -5, -3, 12, 6}
B) D = {3, 12, 7, 6, 2}; R = {-9, -10, -5, -11, -3}
C) D = {-9, -10, -5, -11, -3}; R = {3, 12, 7, 6, 2}
D) D = {-9, -5, -3, 12, 6}; R = {-10, -11, 3, 7, 2}

Question 23

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

A) No
B) Yes

Question 24

Determine whether the equation defines y as a function of x.
y = 2

A) Yes
B) No

Question 25

Find the domain and range.
y =

A)
B)
C)
D)

Question 26

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

A) No
B) Yes

Question 27

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

A) No
B) Yes

Question 28

Evaluate.
If f(x) = , find f(3).

A) 100
B) -8
C) -16
D) 16

Question 29

Find the domain and range.
y = 4x - 11

A)
B)
C)
D)

Question 30

Find the domain and range.
x =

A)
B)
C)
D)

Question 31

Find the domain and range.
{(x, y) y = 7}

A)
B)
C)
D)

Question 32

Find the domain and range.
{(9, -2), (-2, 2), (2, 3), (-3, 7)}

A) D = {-3, -2, 2, 9}; R = {7, 2, 2, 3, -2}
B) D = {7, 2, 3, -2}; R = {-3, -2, 2, 9}
C) D = {-3, -2, 2, 9}; R = {7, 2, 3, -2}
D) D = {-3, -2, 2, 9}; R = {7, 7, 2, 3, -2}

Question 33

Find the domain and range.
y =

A)
B)
C)
D)

Question 34

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

A) Yes
B) No

Question 35

Find the domain and range.
{(-4, 7), (-4, 6), (-9, -2), (-1, -4), (2, 3)}

A) D = {-9, -3, -1, -4, 2}; R = {-2, -4, 6, 3, 7}
B) D = {-2, -4, 6, 3, 7}; R = {-9, -9, -1, -4, 2}
C) D = {-9, -1, -4, 2}; R = {-2, -4, 6, 3, 7}
D) D = {-9, -9, -1, -4, 2}; R = {-2, -4, 6, 3, 7}

Question 36

Determine whether the equation defines y as a function of x.
y = 9x + 5

A) Yes
B) No

Question 37

Determine whether the equation defines y as a function of x.
= (x - 3)(x + 9)

A) Yes
B) No

Question 38

Determine whether the equation defines y as a function of x.
y = + 3

A) No
B) Yes

Question 39

Determine whether the equation defines y as a function of x.
y = 8 - 9x - 9

A) No
B) Yes

Question 40

Determine whether the equation defines y as a function of x.
x = - 2

A) No
B) Yes

Question 41

Find the difference quotient, , for the function and simplify it.
q(x) =

A)
B)
C)
D)

Question 42

Evaluate.
If f(x) = 2 + x, find f(x + h) - f(x).

A)
B)
C)
D)

Question 43

Evaluate.
If f = (2, -6), (5, -3), (6, -1) and g(x) = 4x + 9, find f(5) + g(5).

A) 34
B) 10
C) 62
D) 26

Question 44

Solve the problem.
Bob wants to fence in a rectangular garden in his yard. He has 64 feet of fencing to work with and wants to use it all. If the garden is to be x feet wide, express the area of the garden as a function of x.

A)
B)
C)
D)

Question 45

Solve the problem.
In January 1983, Anna starts a new job and makes an annual salary of $38,000. By January 1986 her annual salary has increased to $46,200, and by January 1996 it has increased to $240,200. What is the average rate of
Change of her salary between January 1986 and January 1996?

A) $19,400 per year
B) $25,220 per year
C) $15,554 per year
D) $20,220 per year

Question 46

Solve the problem.
Suppose that a rectangular yard has a width of x and a length of 8x. Write the perimeter P as a function of x.

A) P = 18x
B)
C) P = 9x
D)

Question 47

Solve the problem.
Suppose that a circular coin has a circumference of C, a radius of r, and a diameter of d. Write C as a function of d.

A)
B)
C)
D)

Question 48

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 400 feet. After 50 minutes the bell is at a depth of 1600 feet. What is the average rate of lowering per minute?

A) 31.6 ft per minute
B) 24.0 ft per minute
C) 32.0 ft per minute
D) 0.03 ft per minute

Question 49

Evaluate.
If f(x) = find f(-9).

A) -5
B) 13
C) 5
D) -13

Question 50

Evaluate.
Find f(a + 3) when f(x) = + 5.

A) a2 + 9
B)
C)
D)

Question 51

Find the difference quotient, , for the function and simplify it.
p(x) = 2 -

A)
B)
C)
D)

Question 52

Find the difference quotient, , for the function and simplify it.
f(x) = 7x - 11

A)
B) 7
C) 11
D) -7h

Question 53

Evaluate.
Find g(a - 1) when g(x) = 4x + 2.

A) 4a + 2
B) 4a - 2
C)
D) 4a + 1

Question 54

Evaluate.
If f(x) = + 4x - 3, find f(4).

A) 173
B) 97
C) 53
D) 176

Question 55

Find the difference quotient, , for the function and simplify it.
a(x) =

A)
B)
C)
D)

Question 56

Find the difference quotient, , for the function and simplify it.
g(x) = + 10x - 5

A) 10x + 6 + 20h
B) 20x + 10 + 10h
C)
D) 20x + 10

Question 57

Evaluate.
Find g(a + 1) when g(x) = x - 3.

A)
B)
C)
D)

Question 58

Solve the problem.
Elissa wants to set up a rectangular dog run in her backyard. She has 30 feet of fencing to work with and wants to use it all. If the dog run is to be x feet long, express the area of the dog run as a function of x.

A)
B)
C)
D)

Question 59

Evaluate.
If f(x) = - 4x - 2, find f(6).

A) 4
B) 156
C) 154
D) 174

Question 60

Evaluate.
Find f(k - 1) when f(x) = + 5x - 3.

A)
B)
C)
D)

Question 61

Solve the problem.
Suppose the sales of a particular brand of appliance satisfy the relationship S(x) = 60x + 3300, where S(x) represents the number of sales in year x, with x = 0 corresponding to 1982. In what year would the sales be
3720?

A) 1989
B) 1986
C) 1987
D) 1988

Question 62

Graph the equation by plotting ordered pairs of numbers.

A)
B)
C)
D)

Question 63

Solve the problem.
The mathematical model C = 700x + 50,000 represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached $470,000?

A) 743 items
B) 529 items
C) 600 items
D) 469,300 items

Question 64

Solve the problem.
Sue wants to put a rectangular garden on her property using 90 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the
Rectangle. (Fencing is then needed only on the other three sides.) Let x represent the length of the side of the
Rectangle along the river. Express the garden's area as a function of x.

A)
B)
C)
D)

Question 65

Graph the function.

A)
B)
C)
D)

Question 66

Solve the problem.
Let C(x) = 600 + 20x be the cost to manufacture x items. Find the average cost per item, to the nearest dollar, to produce 50 items.

A) $1625
B) $32
C) $248
D) $1550

Question 67

Graph the function.

A)
B)
C)
D)

Question 68

Graph the equation by plotting ordered pairs of numbers.

A)
B)
C)
D)

Question 69

Solve the problem.
The revenue in dollars from the sale of concert tickets at x dollars each is given by the function R(x) = 19,000x - 500x2. Find the difference quotient when x = 20 and h = 0.1. Interpret the result.

A) At 20 per ticket, revenue is increasing at $1050 per dollar change in ticket price.
B) At 20 per ticket, revenue is increasing at $105 per dollar change in ticket price.
C) At 20 per ticket, revenue is decreasing at $105 per dollar change in ticket price.
D) At 20 per ticket, revenue is decreasing at $1050 per dollar change in ticket price.

Question 70

Graph the function.

A)
B)
C)
D)

Question 71

Graph the equation by plotting ordered pairs of numbers.

A)
B)
C)
D)

Question 72

Solve the problem.
A rectangular sign is being designed so that the length of its base, in feet, is 18 feet less than 4 times the height, h. Express the area of the sign as a function of h.

A)
B)
C)
D)

Question 73

Graph the equation by plotting ordered pairs of numbers.

A)
B)
C)
D)

Question 74

Solve the problem.
Let R(x) = -19x + 175 represent the number of students present in a large class, where x represents the number of hours of study required weekly. What is the rate of change of the number of students in the class with respect
To the number of hours of study?

A) 175
B) 19
C) -175
D) -19

Question 75

Graph the equation by plotting ordered pairs of numbers.

A)
B)
C)
D)

Question 76

Graph the equation by plotting ordered pairs of numbers.
-2x = y - 1

A)
B)
C)
D)

Question 77

Solve the problem.
Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $4500 in 1982 and $63,000 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S(x).

A) S(x) = 58,500x + 4500
B) S(x) = 11,700x + 4500
C) S(x) = 11,700x + 63,000
D) S(x) = 58,500x + 63,000

Question 78

Solve the problem.
The cost of manufacturing a molded part is related to the quantity of parts produced during a production run. When 100 parts are produced, the cost is $300. When 300 parts are produced, the cost is $1900. What is the
Average cost per part?

A) $0.13 per part
B) $8.00 per part
C) $9.00 per part
D) $5.33 per part

Question 79

Graph the function.

A)
B)
C)
D)

Question 80

Graph the equation by plotting ordered pairs of numbers.

A)
B)
C)
D)