Deck 1: Functions and Their Graphs

Question 1

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

- $y=\frac{1}{x}$

A) function
B) not a function

Answer 1

function

Question 2

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

- $x+7 y=5$

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.

- $\{(-1,-3),(-2,-2),(-2,0),(2,2),(14,4)\}$

A) function
domain: $\{-3,-2,0,2,4\}$
range: $\{-1,2,-2,14\}$

B) function
domain: $\{-1,2,-2,14\}$
range: $\{-3,-2,0,2,4\}$

C) $\text { not a function }$

Answer 3

$\text { not a function }$

Question 4

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

- $y=|x|$

A) function
B) not a function

Question 5

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

- $y=\pm \sqrt{1-5 x}$

A) function
B) not a function

Question 6

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

- $\begin{aligned}4 & \rightarrow 8 \\9 & \rightarrow 18 \\14 & \rightarrow 28 \\19 & \rightarrow 38\end{aligned}$

A) function
domain: $\{8,18,28,38\}$
range: $\{4,9,14,19\}$

B) function
domain: $\{4,9,14,19\}$
range: $\{8,18,28,38\}$

C) $\text { not a function }$

Question 7

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

- $x=y^{2}$

A) function
B) not a function

Question 8

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

- $y=7 x^{2}-2 x+8$

A) function
B) not a function

Question 9

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

- $-4 x+x^{2}-58=y$

A) function
B) not a function

Question 10

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

- $y=\frac{5 x+3}{x+2}$

A) function
B) not a function

Question 11

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

- $x^{2}=8-x^{2}$

A) function
B) not a function

Question 12

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

-

A)
function
$\text { domain: \{carrots, peas, squash }$
$\text { range: \{Bob. Ann. Dave\} }$


B)
function
$\text { domain: \{Bob, Ann, Dave\} }$
$\text { range: \{carrots, peas, squash\} }$

C)
$\text { not a function }$

Question 13

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

-

A) function
domain: {Ms. Lee, Mr. Bar}
range: $\{$ Bob, Ann, Dave $\}$

B) function
domain: {Bob, Ann, Dave}
range:{Ms. Lee, Mr. Bar}

C) $\text { not a function }$

Question 14

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

- $x^{2}+2 y^{2}=1$

A) function
B) not a function

Question 15

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

- $\{(-4,11),(-3,4),(0,-5),(3,4),(5,20)\}$

A) function
domain: $\{11,4,-5,20\}$
range: $\{-4,-3,0,3,5\}$

B) function
domain: $\{-4,-3,0,3,5\}$
range: $\{11,4,-5,20\}$

C) $\text { not a function }$

Question 16

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

- $(-3,6),(2,3),(3,-3),(8,-1)$

A) function
domain: $\{6,3,-3,-1\}$
range: $\{-3,2,3,8\}$

B) function
domain: $\{-3,2,3,8\}$
range: $\{6,3,-3,-1\}$

C) $\text { not a function }$

Question 17

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

- $\left\{(2.44,3.24),(2.444,-3.2),\left(\frac{7}{3}, 0\right),(2.33,-2)\right\}$

A) function
domain: $\{3.24,-3.2,0,-2\}$
range: $\left\{2.44,2.444, \frac{7}{3}, 2.33\right\}$

B) function
domain: $\left\{2.44,2.444, \frac{7}{3}, 2.33\right\}$
range: $\{3.24,-3.2,0,-2\}$

C) $\text { not a function }$

Question 18

Find the value for the function.

- $\text { Find } f(4) \text { when } f(x)=x^{2}-4 x+3$

A) -3
B) 35
C) 3
D) 29

Question 19

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

- $y=x^{4}$

A) function
B) not a function

Question 20

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

- $y^{2}+x=2$

A) function
B) not a function

Question 21

Find the value for the function.

-Find $- f ( x )$ when $f ( x ) = 2 x ^ { 2 } + 4 x - 4$ .

A) $2 x ^ { 2 } - 4 x - 4$
B) $- 2 x ^ { 2 } - 4 x + 4$
C) $2 x ^ { 2 } - 4 x + 4$
D) $- 2 x ^ { 2 } - 4 x - 4$

Question 22

Solve the problem.

-If a rock falls from a height of 70 meters on Earth, the height H (in meters) after x seconds is approximately $$H ( x ) = 70 - 4.9 x ^ { 2 }$$ When does the rock strike the ground? Round to the nearest hundredth, if necessary.

A) 14.29 sec
B) 2.92 sec
C) 3.78 sec
D) 1.71 sec

Question 23

Find the value for the function.

-Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x + 4 }$

A) $\frac { x ^ { 2 } + 2 x - 6 } { x - 3 }$
B) $\frac { x ^ { 2 } + 2 x + 8 } { x + 5 }$
C) $\frac { x ^ { 2 } - 6 } { x + 5 }$
D) $\frac { x ^ { 2 } + 2 x - 6 } { x + 5 }$

Question 24

Find the value for the function.

-Find $f ( 2 x )$ when $f ( x ) = \sqrt { 2 x ^ { 2 } - 7 x }$ .

A) $\sqrt { 4 x ^ { 2 } - 14 x }$

B) $\sqrt { 4 x ^ { 2 } - 28 x }$

C) $\sqrt { 8 x ^ { 2 } - 14 x }$

D) $2 \sqrt { 2 x ^ { 2 } - 7 x }$

Question 25

Find the value for the function.

-Find $f ( x + h )$ when $f ( x ) = \frac { 9 x + 8 } { 8 x - 3 }$

A) $\frac { 9 x + 8 h } { 8 x - 3 h }$

B) $\frac { 9 x + 9 h + 8 } { 8 x - 3 }$

C) $\frac { 9 x + 17 h } { 8 x + 5 h }$

D) $\frac { 9 x + 9 h + 8 } { 8 x + 8 h - 3 }$

Question 26

Find the value for the function.

-Find $- f ( x )$ when $f ( x ) = | x | + 9$ .

A) $| - x | + 9$
B) $| - x | - 9$
C) $- | x | - 9$
D) $- | x | + 9$

Question 27

Find the value for the function.

- $\text { Find } f(-x) \text { when } f(x)=\frac{x}{x^{2}+1}$

A) $\frac{-x}{x^{2}+1}$

B) $\frac{-x}{x^{2}-1}$

C) $\frac{-x}{-x^{2}+1}$

D) $\frac{x}{-x^{2}+1}$

Question 28

Find the value for the function.

- $\text { Find } f(-x) \text { when } f(x)=2 x^{2}+3 x-2$

A) $2 x^{2}-3 x+2$
B) $2 x^{2}-3 x-2$
C) $-2 x^{2}-3 x+2$
D) $-2 x^{2}-3 x-2$

Question 29

Solve the problem.

-If $f ( x ) = \frac { x - B } { x - A } , f ( 4 ) = 0$ , and $f ( 9 )$ is undefined, what are the values of $A$ and $B$ ?

A) $\mathrm { A } = - 4 , \mathrm {~B} = - 9$
B) $\mathrm { A } = 9 , \mathrm {~B} = 4$
C) $\mathrm { A } = 4 , \mathrm {~B} = 9$
D) $\mathrm { A } = - 9 , \mathrm {~B} = - 4$

Question 30

Find the domain of the function.

- $$f ( x ) = - 9 x - 2$$

A) $\{ x \mid x > 0 \}$
B) $\{ x \mid x \neq 0 \}$
C) $\{ x \mid x \geq 2 \}$
D) all real numbers

Question 31

Find the value for the function.

- $\text { Find } f(-2) \text { when } f(x)=\frac{x^{2}-7}{x-1}$

A) 9
B) $-\frac{4}{3}$
C) $-\frac{11}{3}$
D) 1

Question 32

Solve the problem.

-If $f ( x ) = 9 x ^ { 3 } + 5 x ^ { 2 } - x + C$ and $f ( - 2 ) = 1$ , what is the value of $C$ ?

A) $C = - 53$
B) $C = - 13$
C) $\mathrm { C } = 51$
D) $C = - 93$

Question 33

Find the value for the function.

- $\text { Find } f(-9) \text { when } f(x)=|x|-6$

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

Question 34

Find the value for the function.

-Find $f ( x + h )$ when $f ( x ) = 2 x ^ { 2 } + 3 x - 3$

A) $2 x ^ { 2 } + 2 h ^ { 2 } + 7 x + 7 h - 3$
B) $2 x ^ { 2 } + 2 h ^ { 2 } + 3 x + 3 h - 3$
C) $2 x ^ { 2 } + 4 x h + 2 h ^ { 2 } + 3 x + 3 h - 3$
D) $2 x ^ { 2 } + 2 x h + 2 h ^ { 2 } + 3 x + 3 h - 3$

Question 35

Solve the problem.

-If $f ( x ) = \frac { x - 4 A } { - 12 x + 3 }$ and $f ( - 12 ) = - 4$ , what is the value of $A$ ?

A) $\mathrm { A } = - 144$
B) $A = - 150$
C) $\mathrm { A } = 150$
D) $\mathrm { A } = 144$

Question 36

Find the value for the function.

-Find $f ( 2 x )$ when $f ( x ) = - 2 x ^ { 2 } - 3 x + 1$

A) $- 8 x ^ { 2 } - 6 x + 1$
B) $- 8 x ^ { 2 } - 6 x + 2$
C) $- 4 x ^ { 2 } - 6 x + 2$
D) $- 4 x ^ { 2 } - 6 x + 1$

Question 37

Find the value for the function.

- $\text { Find } f(0) \text { when } f(x)=\sqrt{x^{2}+2 x}$

A) $\sqrt{6}$
B) 0
C) 2
D) $\sqrt{2}$

Question 38

Find the value for the function.

-Find $f ( x - 1 )$ when $f ( x ) = 5 x ^ { 2 } - 3 x + 1$

A) $5 x ^ { 2 } + 2 x + 3$
B) $5 x ^ { 2 } - 13 x + 9$
C) $5 x ^ { 2 } - 13 x + 3$
D) $- 13 x ^ { 2 } + 5 x + 9$

Question 39

Solve the problem.

-If a rock falls from a height of 80 meters on Earth, the height H (in meters) after x seconds is approximately $$H ( x ) = 80 - 4.9 x ^ { 2 }$$ What is the height of the rock when x = 1.5 seconds? Round to the nearest hundredth, if necessary.

A) 72.65 m
B) 68.98 m
C) 91.03 m
D) 69.2 m

Question 40

Find the domain of the function.

- $$f ( x ) = x ^ { 2 } + 2$$

A) $\{ x \mid x > - 2 \}$
B) $\{ x \mid x z - 2 \}$
C) all real numbers
D) $\{ x \mid x \geq - 2 \}$

Question 41

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

- $$f ( x ) = x + 6 ; g ( x ) = 7 x ^ { 2 }$$
Find $f + g$ .

A) $( f + g ) ( x ) = 7 x ^ { 2 } + x + 6 ; \{ x \mid x \neq - 6 \}$
B) $( f + g ) ( x ) = 7 x ^ { 2 } + x + 6$ ; all real numbers
C) $( f + g ) ( x ) = 7 x ^ { 2 } - x - 6$ ; all real numbers
D) $( f + g ) ( x ) = - 7 x ^ { 2 } + x + 6$ ; all real numbers

Question 42

Solve the problem.
Jacey, a commissioned salesperson, earns $140 base pay plus $35 per item sold. Express Jacey's gross salary G as a function of the number x of items sold.

A) G(x) = 35(x + 140)
B) G(x) = 35x + 140
C) G(x) = 140(x + 35)
D) G(x) = 140x +35

Question 43

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

- $$f ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - x$$
Find $f + g$ .

A) $( f + g ) ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 16 x + 64$ ; all real numbers
B) $( f + g ) ( x ) = - x ^ { 2 } - x + 20 ; \{ x \mid x \neq 4 , x \neq - 5 \}$
C) $( f + g ) ( x ) = 4 + x ; \{ x \mid x \neq - 4 \}$
D) $( f + g ) ( x ) = - x ^ { 2 } + x + 12$ ; all real numbers

Question 44

Find the domain of the function.

- $$f ( x ) = \sqrt { 24 - x }$$

A) $\{ x \mid x \neq 24 \}$
B) $\{ x \mid x \leq 2 \sqrt { 6 } \}$
C) $\{ x \mid x \neq 2 \sqrt { 6 } \}$
D) $\{ x \mid x \leq 24 \}$

Question 45

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

- $$f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2$$
Find $\frac { f } { g }$ .

A) $\left( \frac { f } { g } \right) ( x ) = \frac { \sqrt { x } } { 5 x - 2 } ; \{ x \mid x \neq 0 \}$
B) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \geq 0 , \mathrm { x } \neq \frac { 2 } { 5 } \right\}$
C) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 5 \mathrm { x } - 2 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 2 } { 5 } \right\}$
D) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 5 \mathrm { x } - 2 } { \sqrt { \mathrm { x } } } ; \{ \mathrm { x } \mid \mathrm { x } \geq 0 \}$

Question 46

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

- $$f ( x ) = 9 x - 5 ; g ( x ) = 4 x - 8$$
Find $f - g$ .

A) $( f - g ) ( x ) = 13 x - 13 ; \{ x \mid x \neq 1 \}$
B) $( f - g ) ( x ) = 5 x - 13 ; \left\{ x \mid x \neq \frac { 13 } { 5 } \right\}$
C) $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = 5 \mathrm { x } + 3$ ; all real numbers
D) $( f - g ) ( x ) = - 5 x - 3$ ; all real numbers

Question 47

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

-f(x) = 5x - 8

A) 0
B) $5 + \frac { 10 ( \mathrm { x } - 8 ) } { \mathrm { h } }$
C) 5
D) $5 + \frac { - 16 } { \mathrm {~h} }$

Question 48

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

- $$f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }$$
Find $f + g$ .

A) $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$

B) $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \{ x \mid x \neq 0 \}$

C) $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } , x \neq \frac { 6 } { 11 } \right\}$

D) $( f + g ) ( x ) = \frac { 3 x + 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$

Question 49

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

- $$f ( x ) = 3 - 3 x ; g ( x ) = - 5 x + 3$$
Find $f + g$

A) $( f + g ) ( x ) = - 8 x + 6$ ; all real numbers
B) $( f + g ) ( x ) = - 2 x$ ; all real numbers
C) $( f + g ) ( x ) = - 5 x + 3 ; \left\{ x \mid x \neq \frac { 3 } { 5 } \right\}$
D) $( f + g ) ( x ) = 2 x + 6 ; \{ x \mid x \neq 3 \}$

Question 50

Solve the problem.

-Given $f ( x ) = \frac { 1 } { x }$ and $\left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x }$ , find the function $g$ .

A) $g ( x ) = \frac { x - 6 } { x - 4 }$

B) $g ( x ) = \frac { x + 6 } { x + 4 }$

C) $g ( x ) = \frac { x - 4 } { x - 6 }$

D) $g ( x ) = \frac { x + 4 } { x + 6 }$

Question 51

Find the domain of the function.

- $$h ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }$$

A) $\{ x \mid x \neq 2 \}$
B) $\{ x \mid x \neq 0 \}$
C) all real numbers
D) $\{ x \mid x \neq - 3,0,3 \}$

Question 52

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

- $$f ( x ) = \sqrt { 6 - x } ; g ( x ) = \sqrt { x - 2 }$$
Find $f \cdot g$ .

A) $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \neq 2 , x \neq 6 \}$
B) $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid 2 \leq x \leq 6 \}$
C) $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \geq 0 \}$
D) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \sqrt { - \mathrm { x } ^ { 2 } - 12 } ; \{ \mathrm { x } \mid \mathrm { x } \neq 12 \}$

Question 53

Find the domain of the function.

- $\frac { x } { \sqrt { x - 2 } }$

A) $\{ x \mid x > 2 \}$
B) $\{ x \mid x \geq 2 \}$
C) all real numbers
D) $\{ x \mid x \neq 2 \}$

Question 54

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

- $$f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$$
Find $f \cdot g$ .

A) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 5 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2$ ; all real numbers
B) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 6 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2$ ; all real numbers
C) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 2$ ; all real numbers
D) $( f \cdot g ) ( x ) = 10 x ^ { 5 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2 ; \{ x \mid x \neq 0 \}$

Question 55

Find the domain of the function.

- $$f ( x ) = \frac { x } { x ^ { 2 } + 14 }$$

A) $\{ x \mid x \neq - 14 \}$
B) $\{ x \mid x > - 14 \}$
C) $\{ x \mid x \neq 0 \}$
D) all real numbers

Question 56

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

- $$f ( x ) = 7 x + 3 ; g ( x ) = 3 x + 7$$
Find f $\cdot g .$

A) $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 21 ; \{ x \mid x \neq 21 \}$
B) $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 58 x + 21$ ; all real numbers
C) $( f \cdot g ) ( x ) = 10 x ^ { 2 } + 58 x + 10$ ; all real numbers
D) $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 16 x + 21 ; \{ x \mid x \neq 21 \}$

Question 57

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

- $$f ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }$$
Find $\mathrm { f } \cdot \mathrm { g }$ .

A) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { 2 \mathrm { x } + 14 } } { \mathrm { x } } ; \{ \mathrm { x } \mid \mathrm { x } \geq - 7 , \mathrm { x } \neq 0 \}$

B) $( f \cdot g ) ( x ) = \frac { 2 \sqrt { x + 7 } } { x } ; \{ x \mid x \geq - 7 , x \neq 0 \}$

C) $( f \cdot g ) ( x ) = \sqrt { \frac { 9 } { x } } ; \{ x \mid x \neq 0 \}$

D) $( f \cdot g ) ( x ) = \sqrt { \frac { 2 x + 14 } { x } } ; \{ x \mid x \geq - 7 , x \neq 0 \}$

Question 58

Find the domain of the function.

- $$g ( x ) = \frac { 2 x } { x ^ { 2 } - 81 }$$

A) all real numbers
B) $\{ x \mid x \neq 0 \}$
C) $\{ x \mid x > 81 \}$
D) $\{ x \mid x \neq - 9,9 \}$

Question 59

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

- $$f ( x ) = 2 x + 5 ; g ( x ) = 6 x - 1$$
Find $\frac { f } { g }$ .

A) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$
B) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq - \frac { 5 } { 2 } \right\}$
C) $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 2 x + 5 } ; \left\{ x \mid x \neq - \frac { 5 } { 2 } \right\}$
D) $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 1 } { 2 \mathrm { x } + 5 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$

Question 60

Solve the problem.

-Express the gross salary G of a person who earns $35 per hour as a function of the number x of hours worked.

A) $G ( x ) = 35 x ^ { 2 }$
B) $G ( x ) = \frac { 35 } { x }$
C) $G ( x ) = 35 x$
D) $\mathrm { G } ( \mathrm { x } ) = 35 + \mathrm { x }$

Question 61

Solve the problem.
A retail store buys 120 VCRs from a distributor at a cost of $200 each plus an overhead charge of $35 per order. The retail markup is 30% on the total price paid. Find the profit on the sale of one VCR.

A) $6,009.00
B) $60.00
C) $59.91
D) $60.09

Question 62

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

-

A)
function
domain: $\{x \mid-9 \leq x \leq 9\}$
range: $\{y \mid-9 \leq y \leq 9\}$
intercepts: $(-9,0),(0,-9),(0,9),(9,0)$
symmetry: $\mathrm{x}$ -axis, $\mathrm{y}$ -axis

B)
function
domain: $\{x \mid-9 \leq x \leq 9\}$
range: $\{y \mid-9 \leq y \leq 9\}$
intercepts: $(-9,0),(0,-9),(0,9),(9,0)$
symmetry: $x$ -axis, $y$ -axis, origin

C)
function
domain: $\{x \mid-9 \leq x \leq 9\}$
range: $\{y \mid-9 \leq y \leq 9\}$
intercepts: $(-9,0),(0,-9),(0,0),(0,9),(9,0)$
symmetry: origin

D)not a function

Question 63

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

- $$f ( x ) = \frac { 1 } { 7 x }$$

A) $\frac { - 1 } { 7 x ( x + h ) }$
B) $\frac { 1 } { 7 x }$
C) 0
D) $\frac { - 1 } { x ( x + h ) }$

Question 64

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

-For what numbers $x$ is $f ( x ) < 0$ ?

A) $( - \infty , - 6 )$
B) $[ - 10 , - 6 ) , ( 7,10 )$
C) $( - 6 , \infty )$
D) $( - 6,7 )$

Question 65

The graph of a function f is given. Use the graph to answer the question.
Is f(3) positive or negative?

A) positive
B) negative

Question 66

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

- $$f ( x ) = x ^ { 2 } + 3 x + 7$$

A) $2 x + h + 3$
B) 1
C) $2 x + h + 7$
D) $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h + 14 } { h }$

Question 67

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

-

A)
$\begin{array}{l}\text { function } \\\text { domain: all real numbers } \\\text { range: all real numbers } \\\text { intercept: }(0,-3) \\\text { symmetry: none }\end{array}$

B)
$\begin{array}{l}\text { function } \\\text { domain: }\{x \mid x=2 \text { or } x=-3\} \\\text { range: all real numbers } \\\text { intercept: }(-3,0) \\\text { symmetry: } x \text {-axis }\end{array}$

C)
function
domain: all real numbers
range: $\{y \mid y=2$ or $y=-3\}$
intercept: $(0,-3)$
symmetry: none

D)
not a function

Question 68

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

-

A)
function
domain: all real numbers
range: \( \{y \mid y \leq-2 \) or \( y \geq 2\} \)
intercepts: \( (-2,0),(2,0) \)
symmetry: \( y \)-axis\[\begin{array} { l l }

B)
function
domain: \( \{x \mid-2 \leq x \leq 2\} \)
range: all real numbers
intercepts: \( (-2,0),(2,0) \)
symmetry: \( \mathrm{x} \)-axis, \( y \)-axis

C)
function
domain: \( \{x \mid x \leq-2 \) or \( x \geq 2\} \)
range: all real numbers
intercepts: \( (-2,0),(2,0) \)
symmetry: \( \mathrm{x} \)-axis, \( \mathrm{y} \)-axis, origirn

D)
\(\text { not a function }\)

Question 69

The graph of a function f is given. Use the graph to answer the question.
Use the graph of f given below to find f(10).

A) 12
B) 10
C) 20
D) 0

Question 70

The graph of a function f is given. Use the graph to answer the question.
Is f(8) positive or negative?

A) positive
B) negative

Question 71

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

-For what numbers x is f(x) > 0?

A) $( - 60 , \infty )$
B) $( - \infty - 60 )$
C) $[ - 100 , - 60 ) , ( 70,100 )$
D) $( - 60,70 )$

Question 72

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

-For what numbers x is f(x) = 0?

A) $- 15$
B) $( - 25 , - 15 ) , ( 17.5,25 )$
C) $( - 15,17.5 )$
D) $- 15,17.5,25$

Question 73

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

-What is the y-intercept?

A) $- 8$
B) 10
C) 7
D) $- 6$

Question 74

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

-

A)
$\begin{array}{l}\text { function } \\\text { domain: }\{x \mid-\pi \leq x \leq \pi\} \\\text { range: }\{y \mid-1 \leq y \leq 1\} \\\text { intercepts: }(-\pi, 0),(0,0),(\pi, 0) \\\text { symmetry: origin }\end{array}$


B)
function
domain: all real numbers
range: $\{y \mid-1 \leq y \leq 1\}$
intercepts: $(-\pi, 0),(0,0),(\pi, 0)$
symmetry: origin

C)
function
domain: $\{x \mid-1 \leq x \leq 1\}$
range: $\{y \mid-\pi \leq y \leq \pi\}$
intercepts: $(-\pi, 0),(0,0),(\pi, 0)$
symmetry: none

D) not function

Question 75

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

-What are the x-intercepts?

A) $- 10 , - 6,7,10$
B) $- 6,7$
C) $- 6,7,10$
D) $- 6$

Question 76

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

-

A)
$\begin{array}{l}\text { function } \\\text { domain: all real numbers } \\\text { range: }\{\mathrm{y} \mid \mathrm{y} \leq 9\} \\\text { intercepts: }(0,-4),(8,0),(0,2) \\\text { symmetry: none }\end{array}$

B)
function
domain: $\{x \mid x \leq 9\}$
range: all real numbers
intercepts: $(-4,0),(0,8),(2,0)$
symmetry: $y$ -axis

C)
function
domain: all real numbers
range: $\{y \mid y \leq 9\}$
intercepts: $(-4,0),(0,8),(2,0)$
symmetry: none

D) not function

Question 77

Solve the problem.

-Suppose that P(x) represents the percentage of income spent on food in year x and I(x) represents income in year x. Determine a function F that represents total food expenditures in year x.

A) $F ( x ) = ( P + I ) ( x )$
B) $F ( x ) = ( P \cdot I ) ( x )$
C) $F ( x ) = ( I - P ) ( x )$
D) $F ( x ) = \left( \frac { I } { P } \right) ( x )$

Question 78

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

-

A)
$\begin{array}{l}\begin{array}{l}\text { function } \\\text { domain: }\{x \mid x \leq 0\} \\\text { range: }\{y \mid y \geq-2\} \\\text { intercepts: }(-2,0),(0,-2),(2,0)\end{array}\\\text { symmetry: } y \text {-axis }\end{array}$

B)
function
domain: $\{x \mid x \geq-2\}$
range: $\{y \mid y \leq 0\}$
intercepts: $(-2,0),(0,-2),(2,0)$
symmetry: none

C)
function
domain: all real numbers
range: all real numbers
intercepts: $(-2,0),(0,-2),(2,0)$
symmetry: none

D) not a function

Question 79

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.

-

A)
$\begin{array}{l}\text { function } \\\text { domain: }\{x \mid x>0\} \\\text { range: all real numbers } \\\text { intercept: }(1,0) \\\text { symmetry: none }\end{array}$

B)
$\begin{array}{l}\text { function } \\\text { domain: all real number: } \\\text { range: }\{\mathrm{y} \mid \mathrm{y}>0\} \\\text { intercept: }(1,0) \\\text { symmetry: none }\end{array}$

C)
$\begin{array}{l}\text { function } \\\text { domain: }\{x \mid x>0\} \\\text { range: all real number } \\\text { intercept: }(0,1) \\\text { symmetry: origin }\end{array}$

D) $\text { not a function }$

Question 80

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

-What is the domain of f?

A) $\{ x \mid x \geq 0 \}$
B) all real numbers
C) $\{ x \mid - 4 \leq x \leq 5.5 \}$
D) $\{ x \mid - 5 \leq x \leq 5 \}$