7) {( 2, 6), ( 1, 3), (0, 2), (1, 3), (3, 11)} A) domain ... · Page 5 Solve the problem. 9) The function P(x) = 0.65x - 57 models the relationship between the number of pretzels

Page 2

7) {(-2, 6), (-1, 3), (0, 2), (1, 3), (3, 11)}

A) domain: {-2, -1, 0, 1, 3}; range: {6, 3, 2, 11} B) domain: {-2, -1, 1, 3}; range: {6, 3, 2, 11} C) domain: {6, 3, 2, 11}; range: {-2, -1, 0, 1, 3} D) domain: {6, 3, 2, 11}; range: {-2, -1, 1, 3}

2 Determine Whether a Relation is a Function

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the relation is a function.

1) {(-1, -6), (2, -5), (4, 9), (8, -5), (10, 3)} A) Function B) Not a function

2) {(-6, 3), (-1, 3), (1, -1), (1, 1)}

A) Not a function B) Function

Full file at https://testbank123.eu/Test-Bank-for-College-Algebra-Essentials-5th-Edition-Blitzer


https://testbank123.eu/Test-Bank-for-College-Algebra-Essentials-5th-Edition-Blitzer

Page 3

3) {(-6, 8), (-6, -5), (2, -8), (6, -8), (9, 6)}


4) {(1, -2), (1, -4), (4, -3), (9, -1), (12, 5)}


5) {(-5, 4), (-2, 9), (4, 8), (5, 2)}

A) Function B) Not a function

6) {(-9, 2), (-9, 5), (2, 7), (4, -1), (9, 4)}


7) {(-7, -1), (-3, -6), (-2, -7), (2, -2)}


8) {(-4, -1), (-3, 7), (2, -8), (2, -9)}


9) {(-6, 6), (-1, 2), (2, -3), (5, 5)}


10) {(-3, -8), (3, 6), (5, -5), (7, -6), (10, 6)}


3 Determine Whether an Equation Represents a Function


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

1) x + y = 49 A) y is a function of x B) y is not a function of x

2) 5x + 7y = 8

A) y is a function of x B) y is not a function of x

3) x2 + y = 25


4) x + y2 = 1


5) x2 + y2 = 36


6) y2 = 6x


7) x = y2


8) y = x3






Page 4

9) y = - x - 8


10) y = 6x - 2


11) x + y3 = 1


12) xy + 6y = 1


13) |x| - y = 6


4 Evaluate a Function


Evaluate the function at the given value of the independent variable and simplify.

1) f(x) = 2x + 4; f(6)

A) 16

B) 36

C) 8

D) 6

2) f(x) = x2 - 4; f(x + 3)

A) x2 + 6x + 5

B) x2 + 9

C) x2 + 6x + 9

D) x2 - 1

3) f(x) = 3x2 - 4x + 2; f(x - 1)

A) 3x2 - 10x + 9

B) -10x2 + 3x + 9

C) 3x2 - 10x + 1

D) 3x2 + 2x + 1

4) g(x) = 3x + 1; g(x + 1)

A) 3x + 4 B) 3x + 1 C) 3x - 1 D) 1 x + 1 3

5) h(x) = x - 11 ; h(15)

A) 4 B) -26 C) 26 D) -4

6) f(x) = x + 19; f(-3)

A) 4 B) -4 C) 2 D) not a real number

7) f(x) = x2 - 3

; f(2) x3 - 6x

A) - 1 4

8) f(x) = x3 + 8

; f(5)

x2 - 4

A) 19 3

B) 1 8

B) 133 25

C) 1 2

C) 125 21

D) - 1

D) 11 7





Page 5

Solve the problem.

9) The function P(x) = 0.65x - 57 models the relationship between the number of pretzels x that a certain vendor sells and the profit the vendor makes. Find P(1000), the profit the vendor makes from selling 1000 pretzels.

A) $593 B) $650 C) $707 D) $943

10) The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is

given by the function C(x) = 0.3x + 27,000. Find C(90,000), the cost of producing 90,000 jars.

A) $54,000 B) $27,000 C) $27.30 D) $90,027





Page 6

5 Graph Functions by Plotting Points


Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the

graph of f.

1) f(x) = x, g(x) = x + 1 y

6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

A) g shifts the graph of f vertically up 1 unit

y 6

5

4

3

2

1

B) g shifts the graph of f vertically down 1 unit

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

C) g shifts the graph of f vertically down 1 unit

y 6

5

4

3

2

1

D) g shifts the graph of f vertically up 1 unit

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 7

2) f(x) = x, g(x) = x - 4

6

5

4

3

2

1

y

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6

A) g shifts the graph of f vertically down 4 units

y 6

5

4

3

2

1

B) g shifts the graph of f vertically down 4 units

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

C) g shifts the graph of f vertically up 4 units

y 6

5

4

3

2

1

D) g shifts the graph of f vertically up 4 units

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 8

3) f(x) = -4x, g(x) = -4x - 4 y

6

5

4

3

2

1

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6


y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6


y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 9

4) f(x) = x2, g(x) = x2 + 1

y 6

5

4

3

2

1

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6

A) g shifts the graph of f vertically up 1 unit

y 6

5

4

3

2

1

B) g shifts the graph of f vertically down 1 unit

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6


y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 10

5) f(x) = 2x2, g(x) = 2x2 - 2

y 6

5

4

3

2

1

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6


y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6


y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 11

6) f(x) = x , g(x) = x + 4 y

6

5

4

3

2

1

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6

A) g shifts the graph of f vertically up 4 units

y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

C) g shifts the graph of f vertically down 4 units

y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 12

7) f(x) = x , g(x) = x

6

5

4

3

2

1

- 4 y

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6


B) g shifts the graph of f vertically up 4 units

6 y

6 y

5 5

4 4

3 3

2 2

1 1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6


-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x

-1

-2

-3

-4

-5

-6


6 y 6

y

5 5

4 4

3 3

2 2

1 1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x

-1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 13

8) f(x) = x3, g(x) = x3 + 3

y 6

5

4

3

2

1

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6

A) g shifts the graph of f vertically up 3 units B) g shifts the graph of f vertically down 3 units

6 y

6 y

5 5

4 4

3 3

2 2

1 1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x

-1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6


y 6

5

4

3

2

1

D) g shifts the graph of f vertically down 3 units

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 14

9) f(x) = x, g(x) = x + 3 y

6

5

4

3

2

1

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6

A) g shifts the graph of f vertically up 3 units

y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6


y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 15

10) f(x) = x, g(x) = x - 1 y

6

5

4

3

2

1

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6

A) g shifts the graph of f vertically down 1 unit

y 6

5

4

3

2

1

B) g shifts the graph of f vertically up 1 unit

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6


y 6

5

4

3

2

1


y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 16

11) f(x) = x, g(x) = x + 1 y

6

5

4

3

2

1

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6

A) g shifts the graph of f 1 unit to the left

y 6

5

4

3

2

1

B) g shifts the graph of f 1 unit to the right

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

C) g shifts the graph of f vertically up 1 unit

y 6

5

4

3

2

1

D) g shifts the graph of f vertically down 1 unit

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 17

12) f(x) = x, g(x) = x - 1 y

6

5

4

3

2

1

x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1

-2

-3

-4

-5

-6

A) g shifts the graph of f 1 unit to the right

y 6

5

4

3

2

1

B) g shifts the graph of f 1 unit to the left

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

C) g shifts the graph of f vertically up 1 unit

y 6

5

4

3

2

1

D) g shifts the graph of f vertically down 1 unit

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6





Page 18

6 Use the Vertical Line Test to Identify Functions


Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.

1) y

x

A) function B) not a function

2)

y

x


3)

y

x

A) not a function B) function





Page 19

4) y

x


5)

y

x


6)

y

x






Page 20

7) y

x


8)

y

x


9)

y

x






Page 21

10) y

x


11)

y

x


12)

y

x






Page 22

13) y

x


7 Obtain Information About a Function from Its Graph


Use the graph to find the indicated function value.

1) y = f(x). Find f(-1)

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) 2.5 B) -2.5 C) 0.3 D) -0.3

2) y = f(x). Find f(3).

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) 1.5 B) 3 C) 9 D) -3





Page 23

3) y = f(x). Find f(-2)

5

y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) 2 B) -2 C) 5 D) 1.25

4) y = f(x). Find f(4)

12

10

8

6

4

2

-5 -4 -3 -2 -1

-2

-4

-6

-8

-10

-12

y

1 2 3 4 5 x

A) 9 B) 7 C) -9 D) 1.5

5) y = f(x). Find f(-4)

13 y

12

11

10

9

8

7

6

5

4

3

2

1

-5 -4 -3 -2 -1 -1 1 2 3 4 5 x

A) 0 B) 9 C) 4 D) 3





Page 23

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use

the graph to answer the question.

6) Does the graph represent a function?

A) yes B) no

7) If f represents the function, find f(1990).

A) approximately 26% B) approximately 28% C) approximately 22.5% D) approximately 21%

8) If f(x) = 26%, what year is represented by x?

A) 1990 B) 1985 C) 1995 D) 1980

9) Between what two years is the difference in function values equal to 5%?

A) between 1980 and 1985 B) between 1985 and 1990 C) between 1970 and 1975 D) between 1960 and 1965





Page 24

8 Identify the Domain and Range of a Function from Its Graph


Use the graph to determine the function's domain and range.

1) y

6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

A) domain: (-∞, ∞)

range: (-∞, ∞)

B) domain: (-∞, ∞)

range: y = -5

C) domain: x = - 5 2

range: (-∞, ∞)

D) domain: x = - 5 2

range: y = -5

2)

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

A) domain: (-∞, ∞)

range: [-5, ∞) C) domain: (-∞, ∞)

range: (-∞, ∞)

B) domain: [4, ∞)

range: [-5, ∞) D) domain: (-∞, 4) or (4, ∞)

range: (-∞, -5) or (-5, ∞)





Page 25

3) y

6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

A) domain: (-∞, ∞)

range: (-∞, 4] C) domain: (-∞, 5]

range: (-∞, 4]

B) domain: (-∞, ∞)

range: (-∞, ∞) D) domain: (-∞, 5) or (5, ∞)

range: (-∞, 4) or (4, ∞)

4)

y 6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 x -1

-2

-3

-4

-5

-6

A) domain: [0, ∞)

range: [-2, ∞)

B) domain: [0, ∞)

range: (-∞, ∞)

C) domain: (-∞, ∞)

range: [-2, ∞)

D) domain: [0, ∞)

range: [0, ∞)





Page 26

5) y 10

8

6

4

2

-10 -8 -6 -4 -2 2 4 6 8 x -2

-4

-6

-8

-10

A) domain: (-∞, ∞)

range: [0, 4]

B) domain: (-∞, ∞)

range: [2, 4]

C) domain: [0, 4]

range: (-∞, ∞)

D) domain: [2, 4]

range: (-∞, ∞)

9 Identify Intercepts from a Function's Graph.


Identify the intercepts. 1)

y

10

5

-10 -5 5 10 x

-5

-10

A) (-2, 0), (0, 6) B) (2, 0), (0, 6) C) (-2, 0), (0, -6) D) (-6, 0), (0, 6)

2)

y

10

5

-10 -5 5 10 x

-5

-10

A) (2, 0), (0, 6) B) (-2, 0), (0, 6) C) (2, 0), (0, -6) D) (-6, 0), (0, 6)





Page 27

3) y

10

5

x -10 -5 5 10

-5

-10

A) (1, 0), (0, -7) B) (-1, 0), (0, -7) C) (1, 0), (0, 7) D) (-7, 0), (0, 7)

4)

y

10

5

-10 -5 5 10 x

-5

-10

A) (5, 0), (-5, 0), (0, 4), (0, -4) B) (5, 0), (-5, 0)

C) (0, 4), (0, -4) D) (4, 0), (-4, 0), (0, 5), (0, -5)

5)

y

10

5

-10 -5 5 10 x

-5

-10

A) (-2, 0), (0, 8) B) (-2, 0), (0, -8) C) (2, 0), (0, 8) D) (-2, -2), (8, 8)





Page 28

6) y

10

5

x -10 -5 5 10

-5

-10

A) (4, 0), (-4, 0), (0, -4) B) (4, 0), (-4, 0)

C) (0, -4) D) (4, 0), (-4, 0), (0, 0)

2.2 More on Functions and Their Graphs

1 Identify Intervals on Which a Function Increases, Decreases, or is Constant


Identify the intervals where the function is changing as requested.

1) Increasing

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) (-2, 2) B) (-3, 3) C) (-2, ∞) D) (-3, ∞)





Page 29

2) Constant

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) (-∞, -1) or (3, ∞) B) (-1, 0) C) (3, ∞) D) (-∞, 0)

3) Increasing

5 y

4

3

2

1

-10 -8 -6 -4 -2 2 4 6 8 10 x -1

-2

-3

-4

-5

A) (3, ∞) B) (3, 6) C) (-2, ∞) D) (-2, 0)

4) Increasing

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) (-2, -1) or (3, ∞) B) (-1, ∞) C) (-2, 1) D) (-1, 3)





Page 30

5) Increasing y

8

4

x -12 -6 6 12

-4

-8

A) (0, 5) B) (1, 6) C) (0, 6) D) (1, 5)

6) Increasing

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) (0, 3) B) (-∞, 0) C) (-∞, -1) D) (-1, 0)

7) Decreasing

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) (-3, -2) B) (0, -2) C) (-∞, -3) D) (-∞, -2)





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8) Decreasing y

8

4

x -12 -6 6 12

-4

-8

A) (5, 12) B) (6, 1) C) (5, 1) D) (6, 12)

9) Decreasing

5 y

4

3

2

1

-10 -8 -6 -4 -2 2 4 6 8 10 x -1

-2

-3

-4

-5

A) (-∞, 3) B) (-∞, -2) C) (0, 3) D) (0, -2)

10) Constant

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) (-1, 1) B) (1, 2) C) (-2, -1) D) (2, ∞)





Page 32

2 Use Graphs to Locate Relative Maxima or Minima


The graph of a function f is given. Use the graph to answer the question.

1) Find the numbers, if any, at which f has a relative maximum. What are the relative maxima?

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) f has a relative maximum at x = 0; the relative maximum is 1

B) f has a relative maximum at x = -3 and 3; the relative maximum is 0 C) f has a relative maximum at x = 3; the relative maximum is 1 D) f has no relative maximum

2) Find the numbers, if any, at which f has a relative minimum. What are the relative minima?

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) f has a relative minimum at x = -1 and 1; the relative minimum is 0

B) f has a relative minimum at x = 0; the relative minimum is 1 C) f has a relative minimum at x = -1; the relative minimum is 0 D) f has no relative minimum





Page 33

A) Odd B) Even C) Neither

2) f(x) = 5x2 + x4

A) Even

B) Odd

C) Neither

3) f(x) = x5 - x4

A) Neither

B) Even

C) Odd

Use the graph of the given function to find any relative maxima and relative minima.

3) f(x) = x3 - 3x2 + 1

5 y

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5 x -1

-2

-3

-4

-5

A) maximum: (0, 1); minimum: (2, -3) B) maximum: (0, 1); minimum: none

C) maximum: none; minimum: (2, -3) D) no maximum or minimum

4) f(x) = x3 - 12x + 2

20 y

16

12

8

4

-5 -4 -3 -2 -1 1 2 3 4 5 x -4

-8

-12

-16

-20

A) minimum: (2, -14); maximum: (-2, 18)

B) maximum: (-2, 18) and (0, 0); minimum: (2, -14) C) maximum: (2, -14); minimum: (-2, 18) D) no maximum or minimum

3 Identify Even or Odd Functions and Recognize Their Symmetries


Determine whether the given function is even, odd, or neither.

1) f(x) = x3 - 4x





Page 34

4) f(x) = -5x5 + x3

A) Odd

B) Even

C) Neither

5) f(x) = x3 + x2 + 3

A) Neither

B) Even

C) Odd

Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a

function that is neither even nor odd.

6)

y

10

8

6

4

2

-10 -8 -6 -4 -2 2 4 6 8 10 x -2

-4

-6

-8

-10

A) Even B) Odd C) Neither

7)

y

10

8

6

4

2

-10 -8 -6 -4 -2 2 4 6 8 10 x -2

-4

-6

-8

-10

A) Neither B) Odd C) Even

8)

y

10

8

6

4

2

-10 -8 -6 -4 -2 2 4 6 8 10 x -2

-4

-6

-8

-10

A) Odd B) Even C) Neither





Page 35

4 Understand and Use Piecewise Functions


Evaluate the piecewise function at the given value of the independent variable.

1) f(x) = 3x + 4 if x < -1 2x - 4 if x ≥ -1

; f(3)

A) 2 B) 5 C) 10 D) 6

2) f(x) = x + 1 if x > 4 ; f(1) -(x + 1) if x ≤ 4

A) -2 B) 2 C) 1 D) 18

3) g(x) =

x2 + 8 if x ≠ 3

x - 3

x + 6 if x = 3

; g(7)

A) 57 4

B) 13 C) 15 4

D) 7

4) h(x) =

x2 - 4 if x ≠ 2

x - 2

x + 2 if x = 2

; h(2)

A) 4 B) undefined C) 0 D) -4

Graph the function.

5) f(x) = x + 4 if x < 1 -1 if x ≥ 1

y

5

-5 5 x

-5

A) B)

y y

5 (1, 5)

5 (1, 5)

-5 (1, -1)

5 x -5 (1, -1)

5 x

-5 -5





Page 36

C)

y

(-1, 5) 5

D)

y

(-1, 5) 5

-5 (-1, -1)

5 x -5 5 x

(-1, -1)

-5 -5





Page 37

6) f(x) = -x + 3 if x < 2 2x - 3 if x ≥ 2

y

5

-5 5 x

-5

A) B)

y y

5 5

-5 5 x -5 5 x

-5 -5

C) D)

y y

5 5

-5 5 x -5 5 x

-5 -5





Page 38

7) f(x) =

x + 2 if -8 ≤ x < 4

-8 if x = 4 -x + 7 if x > 4

y

10

5

-10 -5 5 10 x

-5

-10

A)

y

10

(4, 6)

5 (4, 3)

B)

y

10

(4, 6)

5 (4, 3)

-10 -5 5 10 x -10 -5 5 10 x

(-8, -6)

-5

-10

(4, -8)

(-8, -6)

-5

-10

(4, -8)

C)

y

10

(4, 7)

5

(4, 3)

D)

y

10

(4, 7)

5

(4, 3)

-10 -5 5 10 x -10 -5 5 10 x

(-8, -5)

-5

-10

(4, -8)

(-8, -5)

-5

-10

(4, -8)





Page 39

Based on the graph, find the range of y = f(x).

- 1

x if x ≠ 08) f(x) = 2

-5 if x = 0

10 y

5

-10 -5 5 x

-5 (0, -5)

-10

A) (-∞, 0) or (0, ∞) B) (-∞, ∞)

C) (-10, 10) D) (-∞, 0) or {0} or (0, ∞)

9) f(x) =

4 if -5 ≤ x < -2

|x| if -2 ≤ x < 8

x if 8 ≤ x ≤ 13

10 y

(8, 8)

(-5, 4)

(-2, 54)

(13, 3.6)

(-2, 2)

(8, 2.8)

-10 -5 5 10 15 x

-5

-10

A) [0, 8) B) [0, ∞) C) [0, 13] D) [0, 8]

Solve the problem.

10) Suppose a car rental company charges $110 for the first day and $60 for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(4.5).

A) $350 B) $320 C) $380 D) $270

11) Suppose a life insurance policy costs $20 for the first unit of coverage and then $5 for each additional unit

of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?

A) $65 B) $70 C) $50 D) $30

12) A salesperson gets a commission of $400 for the first $10,000 of sales, and then $200 for each additional

$10,000 or partial of sales. Let S(x) represent the commission on x dollars of sales. Find the value of S(85,000).

A) $2000 B) $1900 C) 2100 D) $1700





Page 40

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

13) A gas company has the following rate schedule for natural gas usage in single-family residences:

Monthly service charge $8.80

Per therm service charge

1st 25 therms $0.6686/therm Over 25 therms $0.85870/therm

What is the charge for using 25 therms in one month?

What is the charge for using 45 therms in one month?

Construct a function that gives the monthly charge C for x therms of gas.

14) An electric company has the following rate schedule for electricity usage in single-family residences:


Per kilowatt service charge

1st 300 kilowatts $0.11589/kW Over 300 kilowatts $0.13321/kW

What is the charge for using 300 kilowatts in one month?

What is the charge for using 375 kilowatts in one month?

Construct a function that gives the monthly charge C for x kilowatts of electricity.

15) One Internet service provider has the following rate schedule for high-speed Internet service:


1st 50 hours of use free

Next 50 hours of use $0.25/hour Over 100 hours of use $1.00/hour

What is the charge for 50 hours of high-speed Internet use in one month?



16) The wind chill factor represents the equivalent air temperature at a standard wind speed that would

produce the same heat loss as the given temperature and wind speed. One formula for computing the

equivalent temperature is

W(t) =

t

33 - (10.45 + 10 v - v)(33 - t )

22.04

33 - 1.5958(33 - t)

if 0 ≤ v < 1.79

if 1.79 ≤ v < 20

if v ≥ 20

where v represents the wind speed (in meters per second) and t represents the air temperature (°C).

Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round

the answer to one decimal place.)





Page 41

17) A cellular phone plan had the following schedule of charges:

Basic service, including 100 minutes of calls $20.00 per month

2nd 100 minutes of calls $0.075 per minute Additional minutes of calls $0.10 per minute

What is the charge for 200 minutes of calls in one month?

What is the charge for 250 minutes of calls in one month?

Construct a function that relates the monthly charge C for x minutes of calls.

5 Find and Simplify a Function's Difference Quotient


Find and simplify the difference quotient f(x + h) - f(x)

, h ≠ 0 for the given function. h

1) f(x) = 8x - 3

A) 8 B) 8 + -6

h

C) 8 + 16(x -

3) h

D) 0

2) f(x) = 6x2

A) 6(2x+h) B) 12

+ x + 6h C) 6(2x2 + 2xh + h2)

D) 6

h h

3) f(x) = 8

A) 0 B) 1 C) 1 + 16

h

D) 8

4) f(x) = 1 2x

A) -1 2x (x + h)

B) -1 x (x + h)

C) 1 2x

D) 0

5) f(x) = x2 + 9x - 2

A) 2x + h + 9 B) 2x2 + 2x + 2xh + h2 + h - 4

h

C) 2x + h - 2 D) 1

2.3 Linear Functions and Slope

1 Calculate a Line's Slope


Find the slope of the line that goes through the given points.

1) (-9, 5), (8, -2)

A) - 7 17

B) - 17 7

C) - 3 D) 7 17





Page 42

2) (-4, 6), (-4, -9)

A) Undefined B) 0 C) 3 8

D) - 15 8

3) (-3, 3), (-2, 3)

A) 0 B) Undefined C) - 6 5

D) 6

4) (-2, 9), (-1, -2)

A) - 11 B) - 1 11

C) - 7 3

D) 11

5) (7, 8), (6, -4)

A) 12 B) - 1 10

C) 1 12

D) - 10

6) (1, -3), (-8, -3)

A) 0 B) 2 C) 3 D) 6

7) (3, 1) and ( 4

, 3) 5

A) - 10 11

B) - 20 11

C) - 11 10

D) 11 10

8) ( 3

, -4) and ( 3

, 4) 4 4

A) Undefined B) 0 C) 15 32

D) 32 15

2 Write the Point-Slope Form of the Equation of a Line


Use the given conditions to write an equation for the line in point-slope form.

1) Slope = -3, passing through (5, 7) A) y - 7 = -3(x - 5) B) y + 7 = -3(x + 5) C) x - 7 = -3(y - 5) D) y = -3x + 22

2) Slope = -3, passing through (-8, 6)

A) y - 6 = -3(x + 8) B) y + 6 = -3(x - 8) C) x - 6 = -3(y + 8) D) y = -3x - 18

3) Slope = 4

, passing through (7, 4) 5

A) y - 4 = 4

(x - 7) B) y + 4 = 4

(x + 7) C) x - 4 = 4

(y - 7) D) y = 4

x + 7 5 5 5 5

4) Passing through (3, 2) and (4, 7)

A) y - 2 = 5(x - 3) or y - 7 = 5(x - 4) B) y - 2 = 5(x - 4) or y - 7 = 5(x - 3) C) y + 2 = 5(x + 3) or y + 7 = 5(x + 4) D) y - 2 = 3(x + 3) or y - 7 = 4(x - 2)





Page 43

5) Passing through (-5, -3) and (-3, -8)

A) y + 3 = - 5

(x + 5) or y + 8 = - 5

(x + 3) B) y + 3 = - 5

(x + 3) or y + 8 = - 5

(x + 5) 2 2 2 2

C) y - 3 = - 5

(x - 5) or y - 8 = - 5

(x - 3) D) y + 3 = - 5

x - 5 or y + 8 = - 5

x + 3 2 2 2 2

6) Passing through (1, -6) with x-intercept = -1

A) y + 6 = - 3(x - 1) or y = - 3(x + 1) B) y - 6 = - 3(x + 1) or y = - 3(x + 1) C) y + 6 = - 3(x - 1) or y = - 3(x - 1) D) y - 1 = - 3x or y - 6 = - 3(x + 1)

3 Write and Graph the Slope-Intercept Form of the Equation of a Line


Use the given conditions to write an equation for the line in slope-intercept form.

1) Slope = -3, passing through (7, 4) A) y = -3x + 25 B) y = -3x - 25 C) y - 4 = -3x - 7 D) y - 4 = x - 7

2) Slope = 2, passing through (-6, 4)

A) y = 2x + 16 B) y = 2x - 16 C) y - 4 = 2x + 6 D) y - 4 = x + 6

3) Slope = 6

, passing through (5, 5) 7

A) y = 6

x + 5 B) y =

6 x -

5 C) y = mx + 5 D) y =

6 x + 5

7 7 7 7 7 7

4) Slope = 5

, y-intercept = 2 9

A) f(x) = 5

x + 2 B) f(x) = - 5

x - 2 C) f(x) = 5

x - 2 D) f(x) = 9

x + 18

9 9 9 5 5


A) y = - 1

x + 11 B) y = mx +

11 C) y - 3 = - 1

(x - 2) D) y = 1

x + 11

3 3 3 3 3 3


A) y = - 3x + 11 B) y = mx + 11 C) y - 5 = - 3(x - 2) D) y = 3x + 11

7) Passing through (-2, -5) and (-6, -6)

A) y = 1

x - 9 B) y = mx -

9 C) y + 5 = 1

(x + 2) D) y = - 1

x - 9

4 2 2 4 4 2





Page 44

Graph the line whose equation is given.

8) y = 3x - 2

6

5

4

3

2

1

-6 -5 -4 -3 -2 --11

-2

-3

-4

-5

-6

y

1 2 3 4 5 6 x

A) B)

6

y 6

y

5 5 4 4 3 3 2 2 1 1

-6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x -6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x

-2 -2 -3 -3 -4 -4 -5 -5 -6 -6

C) D)

6

y 6

y

5 5 4 4 3 3 2 2 1 1

-6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x -6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x

-2 -2 -3 -3 -4 -4 -5 -5 -6 -6





Page 45

6 5

4

3

2

1

-6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x

-2 -3

-4

-5

-6

9) y = -3x + 2 y

A) B)

6

y 6

y

5 5 4 4 3 3 2 2 1 1

-6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x -6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x

-2 -2 -3 -3 -4 -4 -5 -5 -6 -6

C) D)

6

y 6

y

5 5 4 4 3 3 2 2 1 1

-6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x -6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x

-2 -2 -3 -3 -4 -4 -5 -5 -6 -6





Page 46

10) y = 3

x + 2 5

y 6

5

4

3

2

1

x -6 -5 -4 -3 -2 --11

-2

-3

-4

-5

-6

1 2 3 4 5 6

A) B)

6

y 6

y

5 5 4 4 3 3 2 2 1 1

-6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x -6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x

-2 -2 -3 -3 -4 -4 -5 -5 -6 -6

C) D)

6

y 6

y

5 5 4 4 3 3 2 2 1 1

-6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x -6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x

-2 -2 -3 -3 -4 -4 -5 -5 -6 -6





Page 47

11) y = - 2

x - 1 5

y 6

5

4

3

2

1

x -6 -5 -4 -3 -2 --11

-2

-3

-4

-5

-6

1 2 3 4 5 6

A) B)

6

y 6

y

5 5 4 4 3 3 2 2 1 1

-6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x -6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x

-2 -2 -3 -3 -4 -4 -5 -5 -6 -6

C) D)

6

y 6

y

5 5 4 4 3 3 2 2 1 1

-6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x -6 -5 -4 -3 -2 --11 1 2 3 4 5 6 x

-2 -2 -3 -3 -4 -4 -5 -5 -6 -6





Page 48

4 Graph Horizontal or Vertical Lines


Graph the equation in the rectangular coordinate system.

1) x = 3

5 y

4

3

2

1

-5 -4 -3 -2 -1 -1

1 2 3 4 5 x

-2

-3

-4

-5

A) B)

5 y

5 y

4 4

3 3

2 2

1 1

-5 -4 -3 -2 -1 -1

1 2 3 4 5 x -5 -4 -3 -2 -1 -1

1 2 3 4 5 x

-2 -2

-3 -3

-4 -4

-5 -5

C) D)

5 y

5 y

4 4

3 3

2 2

1 1

-5 -4 -3 -2 -1 -1

1 2 3 4 5 x -5 -4 -3 -2 -1 -1

1 2 3 4 5 x

-2 -2

-3 -3

-4 -4

-5 -5





Page 49

2) y = 2

y 5

4

3

2

1

x -5 -4 -3 -2 -1 1 2 3 4 5 -1

-2

-3

-4

-5

A) B)

y

5 y

5

4 4

3 3

2 2

1 1

-5 -4 -3 -2 -1 -1

1 2 3 4 5 x -5 -4 -3 -2 -1 -1

1 2 3 4 5 x

-2 -2

-3 -3

-4 -4

-5 -5

C) D)

5 y

5 y

4 4

3 3

2 2

1 1

-5 -4 -3 -2 -1 -1

1 2 3 4 5 x -5 -4 -3 -2 -1 -1

1 2 3 4 5 x

-2 -2

-3 -3

-4 -4

-5 -5





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