Deck 4: Additional Topics With Functions

Question 1

$$f ( x ) = x ^ { 2 } , g ( x ) = \frac { 1 } { 5 } x ^ { 2 }$$

A)

B)
C)

D)

Answer 1

A

Question 2

$f(x)=|x|, \quad g(x)=|x-2|$

A)

B)

C)

D)

Answer 2

D

Question 3

$f(x)=x^{2}, g(x)=x^{2}-6$

A)

B)


C)

D)

Answer 3

A

Question 4

Fill in each blank with the appropriate response.
The graph of $y = - 6 ( x - 2 ) ^ { 2 } + 8$ can be obtained from the graph of $y = x ^ { 2 }$ by shifting horizontallyــــــــــ units to theـــــــــــ , vertically stretching by a factor ofــــــــــ , reflecting across the ــــــــــــ-axis, and shifting vertically ـــــــــunits in the ــــــــdirection.

A) 2; right; 8; y; 6; downward
B) 2; right; 8; x; 6; upward
C) 2; right; 6; x; 8; upward
D) 2; left; 6; x; 8; upward

Question 5

Fill in each blank with the appropriate response.
The graph of $\mathrm { y } = 2 \sqrt [ 3 ] { \mathrm { x } - 1 } - 3$ can be obtained from the graph of $\mathrm { y } = \sqrt [ 3 ] { \mathrm { x } }$ by shifting horizontallyــــــــــ units to theـــــــــ , vertically stretching by a factor ofـــــــــــــــ and shifting vertically ــــــــــــunits in the directionـــــــــــــــــ.

A) 1; left; 3; 2; downward
B) 1; left; 2; 3; downward
C) 1; right; 2; 3; downward
D) 1; right; 3; 2; upward

Question 6

$f(x)=\sqrt{x}, g(x)=\sqrt{x-3}-2$

A)

B)
C)


D)

Question 7

$f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 1 } { x } + 3$

A)
B)
C)
D)

Question 8

$f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{x}+5$

A)

B)

C)

D)

Question 9

$f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 1 } { x + 3 }$

A)
B)
C)
D)

Question 10

Fill in each blank with the appropriate response.

-The graph of $y = - \frac { 1 } { 6 } ( x + 3 ) ^ { 2 } - 8$ can be obtained from the graph of $y = x ^ { 2 }$ by shifting horizontally $\underline{\quad\quad}$ units to the $\underline{\quad\quad}$ vertically compressing by a factor of $\underline{\quad\quad}$ , reflecting across the $\underline{\quad\quad}$ -axis, and shifting vertically $\underline{\quad\quad}$ units in the $\underline{\quad\quad}$ direction.

A) $3 ;$ left; $\frac { 1 } { 6 } ; x ; 8 ;$ downward
B) 3 ; right; $\frac { 1 } { 6 } ; x ; 8 ;$ downward
C) $3 ;$ left; $8 ; x ; \frac { 1 } { 6 } ;$ downward
D) 3 ; right; $\frac { 1 } { 6 } ; \mathrm { x } ; 8$ ; upward

Question 11

Fill in each blank with the appropriate response.
The graph of $y = - 5 ( x + 3 ) ^ { 2 } - 7$ can be obtained from the graph of $y = x ^ { 2 }$ by shifting horizontallyــــــــ units to the , vertically stretching by a factor ofــــــــ , reflecting across theـــــــــــ -axis, and shifting vertically ــــــــــــunits in the ــــــــــــdirection.

A) 3; right; 5; x; 7; downward
B) 3; right; 5; x; 7; upward
C) 3; left; 7; x; 5; downward
D) 3; left; 5; x; 7; downward

Question 12

$f(x)=\sqrt{x}, g(x)=-3 \sqrt{x}$

A)


B)

C)

D)

Question 13

$f(x)=|x| ; g(x)=-4|x|$

A)

B)

C)

D)

Question 14

$f(x)=x^{3}, g(x)=-x^{3}-4$

A)

B)

C)

D)

Question 15

Fill in each blank with the appropriate response.
The graph of $y = - 3 x ^ { 2 }$ can be obtained from the graph of $y = x ^ { 2 }$ by vertically stretching by a factor ofــــــــ and reflecting across the ــــــــــ-axis.

A) $3 ; x$
B) $- 3 ; y$
C) $3 ; y$
D) $- 3 ; x$

Question 16

$$f ( x ) = | x | , g ( x ) = \frac { 1 } { 2 } | x + 6 | - 3$$

A)

B)


C)

D)

Question 17

$f(x)=\sqrt[3]{x}, g(x)=\sqrt[3]{-x}+4$

A)

B)

C)

D)

Question 18

$f(x)=x^{3}, \quad g(x)=(x+4)^{3}$

A)

B)

C)

D)

Question 19

$$f ( x ) = x ^ { 2 } , g ( x ) = - \frac { 1 } { 4 } ( x + 3 ) ^ { 2 } + 4$$

A)

B)

C )

D)

Question 20

$$f ( x ) = x ^ { 2 } , g ( x ) = ( x - 6 ) ^ { 2 } - 5$$

A)

B)


C)

D)

Question 21

The graph of y= $\sqrt [ 3 ] { x }$ is shifted 3.5 units to the left. This graph is then vertically stretched by a factor of 5.1. Finally, the graph is reflected across the x -axis.

A) $y = - 5.1 \sqrt [ 3 ] { x - 3.5 }$
B) $y = 5.1 \sqrt [ 3 ] { x + 3.5 }$
C) $y = - 5.1 \sqrt [ 3 ] { x + 3.5 }$
D) $y = - 3.5 \sqrt [ 3 ] { x + 5.1 }$

Question 22

$y = 0.79 x ^ { 2 } + | x | + 7$

A) x -axis
B) y -axis
C) No symmetry
D) Origin

Question 23

Write the equation of the graph after the indicated transformation(s).
The graph of $y = x ^ { 2 }$ is shifted 3 units to the left. This graph is then vertically compressed by a factor of $\frac { 1 } { 5 }$ and reflected across the $x$ -axis. Finally, the graph is shifted 7 units downward.

A) $y = \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } - 7$
B) $y = - \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } - 7$
C) $y = - \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } + 7$
D) $y = - \frac { 1 } { 5 } ( x + 3 ) ^ { 2 } - 7$

Question 24

Write the equation of the graph after the indicated transformation(s).
The graph of $y = x ^ { 2 }$ is shifted 5 units to the left and 4 units downward.

A) $y = ( x - 5 ) ^ { 2 } - 4$
B) $y = ( x + 5 ) ^ { 2 } - 4$
C) $y = ( x + 4 ) ^ { 2 } - 5$
D) $y = ( x - 4 ) ^ { 2 } + 5$

Question 25

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown.
$f(x)=x^{2}$

A) $y = ( x + 4 ) ^ { 2 }$
B) $y = ( x - 4 ) ^ { 2 }$
C) $y = x ^ { 2 } - 4$
D) $y = ( x - 4 ) ^ { 2 } + 1$

Question 26

Fill in each blank with the appropriate response.
The graph of $y = | x - 4 | + 3$ can be obtained from the graph of $y = | x |$ by shifting horizontally ـــــــــunits to theـــــــــ , and shifting vertically ـــــــــــunits in theــــــــــــــ direction.

A) 3; right; 4 downward
B) 3; right; 4; upward
C) 4; right; 3; upward
D) 4; left; 3; upward

Question 27

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown.
$f(x)=x^{2}$

A) $y = ( x - 5 ) ^ { 2 } - 5$
B) $y = 2 ( x + 5 ) ^ { 2 }$
C) $y = ( x - 2 ) ^ { 2 } - 5$
D) $y = - 2 ( x - 5 ) ^ { 2 }$

Question 28

$y = - 5 x ^ { 3 }$

A) x -axis
B) Origin
C) No symmetry
D) y -axis

Question 29

$y = - 4 x ^ { 3 } + 6 x$

A) x -axis
B) x -axis, y -axis
C) x -axis, origin
D) Origin

Question 30

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown.
$f(x)=x^{2}$

A) $y = ( x + 4 ) ^ { 2 }$
B) $y = ( x - 4 ) ^ { 2 } + 1$
C) $y = x ^ { 2 } - 4$
D) $y = ( x - 4 ) ^ { 2 }$

Question 31

Write the equation of the function g(x) that is transformed from the given function f(x), and whose graph is shown.
$f(x)=|x|$

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

Question 32

Write the equation of the graph after the indicated transformation(s).
The graph of $y = x ^ { 2 }$ is vertically stretched by a factor of 2 , and the resulting graph is reflected across the $x$ -axis.

A) $y = ( x - 2 ) ^ { 2 }$
B) $y = - 2 x ^ { 2 }$
C) $y = 2 x ^ { 2 }$
D) $y = 2 ( x - 2 ) x ^ { 2 }$

Question 33

$x ^ { 2 } + y ^ { 2 } = 9$

A) y -axis, origin
B) x -axis, y -axis, origin
C) Origin
D) x -axis

Question 34

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
$y = - 5 x ^ { 2 } - 1$

A) No symmetry
B) Origin
C) x-axis
D) y-axis

Question 35

Write the equation of the graph after the indicated transformation(s).
The graph of $y = x ^ { 2 }$ is shifted 2 units to the left. This graph is then vertically stretched by a factor of 6 and reflected across the $x$ -axis. Finally, the graph is shifted 8 units downward.

A) $y = - 6 ( x + 8 ) ^ { 2 } - 2$
B) $y = - 6 ( x + 2 ) ^ { 2 } - 8$
C) $y = - 6 ( x - 2 ) ^ { 2 } + 8$
D) $y = - 6 ( x - 2 ) ^ { 2 } - 8$

Question 36

The graph of y= x³ is shifted 3.0 units to the right and then vertically compressed by a factor of 0.7 .

A) y=3.0(x-0.7)³
B) y=0.7 x³+3.0
C) y=0.7(x+3.0)³
D) y=0.7(x-3.0)³

Question 37

The graph of $y = \sqrt { x }$ is shifted 4 units to the left. Then the graph is shifted 9 units upward.

A) $y = \sqrt { x + 9 } + 4$
B) $y = 9 \sqrt { x + 4 }$
C) $y = \sqrt { x + 4 } + 9$
D) $y = \sqrt { x - 4 } + 9$

Question 38

Write the equation of the graph after the indicated transformation(s).
The graph of $y = x ^ { 2 }$ is shifted 4 units to the right. This graph is then vertically stretched by a factor of 6 and reflected across the $x$ -axis. Finally, the graph is shifted 8 units upward.

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

Question 39

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
$y = | 4 x | + 2$

A) No symmetry
B) y-axis
C) x-axis
D) Origin

Question 40

The graph of $y = \sqrt { x }$ is shifted 4 units to the right.

A) $y = \sqrt { x - 4 }$
B) $y = \sqrt { x } + 4$
C) $y = \sqrt { x + 4 }$
D) $y = \sqrt { x } - 4$

Question 41

Determine if the complete graph represents a function that is even, odd, or neither.

A) odd
B) neither
C) even

Question 42

Determine whether the function is even, odd, or neither.
$y = \sqrt { x ^ { 2 } + 5 }$

A) Odd
B) Neither
C) Even

Question 43

Determine if the complete graph represents a function that is even, odd, or neither.

A) neither
B) even
C) odd

Question 44

Determine whether the function is even, odd, or neither.
$f ( x ) = \left| x ^ { 2 } + x \right|$

A) Even
B) Neither
C) Odd

Question 45

Determine whether the function is even, odd, or neither.
$f ( x ) = ( x + 5 ) ( x + 9 )$

A) Odd
B) Neither
C) Even

Question 46

Determine whether the function is even, odd, or neither.
$f ( x ) = 0.83 x ^ { 2 } + | x | - 1$

A) Odd
B) Neither
C) Even

Question 47

Determine whether the function is even, odd, or neither.
$f ( x ) = - 9 x ^ { 3 } + 6 x$

A) Odd
B) Neither
C) Even

Question 48

The year y when sales were s million dollars for a particular electronics company can be modeled by the radical equation $y = 1.4 \sqrt { s - 2 } - 7$ , where $y = 1$ represents 2010 , and so on. Use the model to predict the sales for 2015 to the nearest tenth of a million.

A) $89.2 million
B) $87.2 million
C) $90.2 million
D) $88.2 million

Question 49

A manufacturer's cost is given by $C = 500 \sqrt [ 3 ] { n } + 512$ , where $C$ is the cost and $n$ is the number of parts produced. Describe the transformations needed to obtain the graph of this function from the graph of $y = \sqrt { n }$ .

A) Stretch vertically by a factor of 500 and shift up 512 units.
B) Stretch vertically by a factor of 500 and shift 512 units to the left.
C) Stretch vertically by a factor of 500 and shift 512 units to the right.
D) Shift 500 units to the left and shift up 512 units.

Question 50

The price per unit of a product is $\$ \mathrm { p }$ and the number of units of the product is denoted by $\mathrm { q }$ . The demand function for this commodity is given by $\mathrm { p } = \frac { 20,000 } { \mathrm { q } } - 50$ . Describe the transformations needed to obtain the graph of this function from the graph of $p = \frac { 1 } { q }$ .

A) Stretch vertically by a factor of 20,000 and shift 50 units to the right.
B) Stretch vertically by a factor of 20,000 and shift down 50 units.
C) Shift up 20,000 units and shift 50 units to the right.
D) Stretch vertically by a factor of 20,000, reflect across the x-axis, and shift down 50 units.

Question 51

Determine whether the function is even, odd, or neither.
$y = \frac { 5 } { x }$

A) Odd
B) Neither
C) Even

Question 52

Determine if the complete graph represents a function that is even, odd, or neither.

A) odd
B) neither
C) even

Question 53

y= $\frac { 3 } { x }$

A) x -axis, y -axis, origin
B) Origin
C) y -axis
D) No symmetry

Question 54

Determine whether the function is even, odd, or neither.
$f ( x ) = 5 x ^ { 2 } + 4$

A) Odd
B) Neither
C) Even

Question 55

Determine if the complete graph represents a function that is even, odd, or neither.

A) even
B) neither
C) odd

Question 56

Determine whether the function is even, odd, or neither.
$f ( x ) = x ^ { 3 } - \frac { 1 } { x }$

A) Even
B) Neither
C) Odd

Question 57

y= x+ $\frac { 1 } { x ^ { 4 } }$

A) Origin
B) y-axis, origin
C) y -axis
D) No symmetry

Question 58

The year y when sales were s million dollars for a particular electronics company can be modeled by the radical equation $y = 1.2 \sqrt { s - 4 } - 6$ , where $y = 1$ represents 2010 , and so on. Describe the transformations needed to obtain the graph of this function from the graph of $y = \sqrt { s }$ .

A) Shift 1.2 units to the right, stretch vertically by a factor of 4, and shift down by 6 units.
B) Shift 4 units to the left, stretch vertically by a factor of 1.2, and shift down by 6 units.
C) Shift 4 units down, stretch vertically by a factor of 1.2, and shift 6 units to the right.
D) Shift 4 units to the right, stretch vertically by a factor of 1.2, and shift down by 6 units.

Question 59

Determine if the complete graph represents a function that is even, odd, or neither.

A) odd
B) even
C) neither

Question 60

Determine whether the function is even, odd, or neither.
$y = | x - 4 |$

A) Even
B) Neither
C) Odd

Question 61

For the pair of functions, perform the indicated operation.
$f ( x ) = 3 x + 8 , g ( x ) = 4 x + 6 \quad$ Find $( f \cdot g ) ( x )$

A) $12 x ^ { 2 } + 50 x + 48$
B) $7 x ^ { 2 } + 50 x + 14$
C) $12 x ^ { 2 } + 48$
D) $12 x ^ { 2 } + 38 x + 48$

Question 62

$f ( x ) = x ^ { 2 } + 1 , g ( x ) = 2 x - 7 \quad \text { Find } ( f \cdot g ) ( x )$

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

Question 63

The linear equation y = 82.67x = 1181 provides an approximation of the va;ue (in dollars) of an account opend on january 1, 2010, in the amount of $1181 and earning 7% simple interest, where x = 0 represents january 1, 2010, x=1 represents january 1, 2011, x=2 represents january 1, 2012. and so on. Write an equation that yields the same y-values when the exact year number is entered.

A) y= 82.67(x - 2011) + 1181
B) y= 82.67(2011 - x) + 1181
C) y= 82.67(2010 - x) + 1181
D) y= 82.67(x- 2010) + 1181

Question 64

The linear equation y=443 x+3420 provides an approximation of the annual cost (in dollars) of health insurance for a family of three, where x=1 represents 2011, x=2 represents 2012, and so on. Write an equation that yields the same y -values when the exact year number is entered.

A) y=443(2010-x)+3420
B) y=443(x-2011)+3420
C) y=443(x-2010)+3420
D) y=443(2011-x)+3420

Question 65

The linear equation y=229 x+6320 provides an approximation of the annual cost (in dollars) to rent an apartment at the Leisure Village Retirement Community, where x=1 represents 2011, x=2 represents 2012, and so on. Write an equation that yields the same y-values when the exact year number is entered.

A) y=229(x-2010)+6320
B) y=229(2010-x)+6320
C) y=229(2011-x)+6320
D) y=229(x-2011)+6320

Question 66

Find the specified domain and express it in interval notation.
For $f ( x ) = x ^ { 2 } - 9$ and $g ( x ) = 2 x + 3$ , what is the domain of $\left( \frac { f } { g } \right) ( x )$ ?

A) $( - 3,3 )$
B) All real numbers
C) All real numbers except $- \frac { 3 } { 2 }$
D) $\left[ - \frac { 3 } { 2 } , \infty \right]$

Question 67

$f ( x ) = x ^ { 3 } + 3 x ^ { 2 } , g ( x ) = \sqrt { x - 8 }$ Find (f+g)(x) .

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

Question 68

For the pair of functions, perform the indicated operation.
$f ( x ) = \sqrt { 2 x + 5 } , g ( x ) = \sqrt { 25 x - 16 } \quad$ Find $( f \cdot g ) ( x )$

A) $( 2 x + 5 ) ( 5 x - 4 )$
B) $( \sqrt { 2 x + 5 } ) ( \sqrt { 25 x - 16 } )$
C) $( 2 x + 5 ) ( 25 x - 16 )$
D) $( 5 x - 4 ) ( \sqrt { 2 x + 5 } )$

Question 69

$f ( x ) = 7 - 7 x , g ( x ) = - 5 x ^ { 2 } + 7 \quad \text { Find } ( f + g ) ( x )$

A) $- 12 x ^ { 2 } - 7 x + 14$
B) $- 5 x ^ { 2 } + 7$
C) $- 5 x ^ { 2 } - 7 x + 14$
D) -12 x+14

Question 70

The price per unit of a product is $\mathrm { p }$ and the number of units of the product is denoted by q. The demand function for this commodity is given by $p = \frac { 4000 } { q + 60 }$ . Describe the transformations needed to obtain the graph of this function from the graph of $p = \frac { 1 } { q }$ .

A) Shift 60 units to the left and stretch vertically by a factor of 4000.
B) Shift up 60 units and stretch vertically by a factor of 4000.
C) Shift 60 units to the right and stretch vertically by a factor of 4000.
D) Shift 60 units to the left and shift up 4000 units.

Question 71

The daily cost $C$ (in dollars) of removing pollution from the smokestack of an electric power plant is related to the percent of pollution $p$ removed according to the equation $C = \frac { 16,400 } { 100 - p }$ . Describe the transformations needed to obtain the graph of this function from the graph of $C = \frac { 1 } { \mathrm { p } }$ .

A) Shift 100 units to the left, reflect across either axis,and stretch vertically by a factor of 16,400.
B) Reflect across the p-axis, shift 100 units to the left and shift up 16,400 units.
C) Shift 100 units to the right, reflect across either axis,and stretch vertically by a factor of 16,400.
D) Shift 100 units to the right and stretch vertically by a factor of 16,400.

Question 72

f(x) = $\frac { 5 x - 8 } { 3 } , g ( x ) = \frac { 1 } { x }$ Find (f - g)(x) .

A) $\frac { 5 x - 8 } { 3 - x }$
B) $\frac { 5 x ^ { 2 } - 8 x - 3 } { 3 x }$
C) $\frac { 5 x ^ { 2 } - 8 x + 3 } { 3 x }$
D) $\frac { 5 x ^ { 2 } - 8 x - 1 } { 3 x }$

Question 73

A study in a small town showed that the percent of residents who have college degrees can be modeled by the function $P = 32 x ^ { 0.31 }$ of years from 2015 . , where x is the number of years from 2010 . Rewrite the model with x equal to the number

A) $\mathrm { P } = 32 \mathrm { x } 0.31 + 5$
B) $P = 32 ( x + 5 ) ^ { 0.31 }$
C) $P = 32 ( x - 5 ) ^ { 0.31 }$
D) $P = 32 x ^ { 0.31 } - 5$

Question 74

$f ( x ) = \frac { 5 x - 4 } { 3 } , g ( x ) = \frac { 1 } { x } \quad \text { Find } \left( \frac { f } { g } \right) ( x )$

A) $\frac { 3 x } { 5 x - 4 }$
B) $\frac { 3 } { 5 x ^ { 2 } - 4 x }$
C) $\frac { 5 x ^ { 2 } - 4 x } { 3 }$
D) $\frac { 5 x - 4 } { 3 x }$

Question 75

The number of people present at a stadium holding a big rock concert can be estimated with the following function: $y = 13252 x ^ { 0.74 } + 0.54 x + 102$ where y is the number of people present and x is the amount of time since 3:00 p.m. on the day of the concert. Rewrite the model with x equal to the amount of time since 1.00 p.m.

A) $y = 13,252 ( x - 2 ) ^ { 0.74 } + 0.54 x + 102$
B) $y = 13,252 ( x - 2 ) ^ { 0.74 } + 0.54 ( x - 2 ) + 102$
C) $y = 13,252 ( x + 2 ) ^ { 0.74 } + 0.54 ( x + 2 ) + 102$
D) $y = 13,252 ( x + 2 ) ^ { 0.74 } + 0.54 x + 102$

Question 76

For the pair of functions, perform the indicated operation.
$f ( x ) = 2 x - 2 , g ( x ) = 5 x - 8 \quad$ Find $( f - g ) ( x )$

A) $- 3 x + 6$
B) $- 3 x - 10$
C) $3 x - 6$
D) $7 x - 10$

Question 77

For the pair of functions, perform the indicated operation.
$f ( x ) = 7 x ^ { 2 } - 8 x , g ( x ) = x ^ { 2 } - 2 x - 48 \quad$ Find $\left( \frac { f } { g } \right) ( x )$

A) $\frac { 7 x - 8 } { - 2 }$
B) $\frac { 7 x ^ { 2 } - 8 x } { x ^ { 2 } - 2 x - 48 }$
C) $\frac { 7 - \mathrm { x } } { 48 }$
D) $\frac { 7 x } { x + 1 }$

Question 78

For the pair of functions, perform the indicated operation.
$f ( x ) = 7 - 8 x , g ( x ) = - 4 x + 8 \quad$ Find $( f + g ) ( x )$

A) $3 x$
B) $- 12 x + 15$
C) $- 4 x + 15$
D) $- 4 x + 7$

Question 79

Find the specified domain and express it in interval notation.
For $f ( x ) = x ^ { 2 } - 81$ and $g ( x ) = 2 x + 3$ , what is the domain of $\left( \frac { g } { f } \right) ( x )$ ?

A) $\left[ - \frac { 3 } { 2 } , \infty \right)$
B) All real numbers
C) $\left( - \infty , \frac { 3 } { 2 } \right) \cup \left( - \frac { 3 } { 2 } , \infty \right)$
D) $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$

Question 80

Find the specified domain and express it in interval notation.
For $f ( x ) = 2 x - 5$ and $g ( x ) = \sqrt { x + 8 }$ , what is the domain of $\left( \frac { f } { g } \right) ( x )$ ?

A) $[ 0 , \infty )$
В) $( - 8 , \infty )$
C) $( - 8,8 )$
D) $[ 8 , \infty )$