Question 1

Solve for x.
- log⁡3x=2\log _ { 3 } x = 2log3​x=2

Accepted Answer

A)   6
B)   5
C)   9
D)   8

Question 2

For the given functions f and g, find the composition.
- f(x) =4x+5;g(x) =2x−1f ( x )  = 4 x + 5 ; g ( x )  = 2 x - 1 \quadf(x) =4x+5;g(x) =2x−1  Find  (f∘g) (x) ( f \circ g )  ( x ) (f∘g) (x)

Accepted Answer

A)    8x+18 x + 18x+1 
B)    8x+98 x + 98x+9 
C)    8X+98 X + 98X+9 
D)    8x+48 x + 48x+4

Question 3

Given the values of f and g, find the function value.
- f(19) =14;g(19) =5f ( 19 )  = 14 ; g ( 19 )  = 5 \quadf(19) =14;g(19) =5  Find  (f−g) (19) ( f - g )  ( 19 ) (f−g) (19)

Accepted Answer

A)   13
B)    −10- 10−10 
C)   19
D)   9

Question 4

Determine whether the functions f and g are inverses of each other.
-$f ( x ) = x ^ { 3 } + 2 ; g ( x ) = \sqrt [ 3 ] { x - 2 }$

Accepted Answer

A) True 
 B)False

Question 5

Solve the equation.
- 5x=1255 ^ { x } = 1255x=125

Accepted Answer

A)   2
B)   25
C)   3
D)   4

Question 6

Solve the equation.
- log⁡23+log⁡2x=1\log _ { 2 } 3 + \log _ { 2 } x = 1log2​3+log2​x=1

Accepted Answer

A)    13\frac { 1 } { 3 }31​ 
B)    32\frac { 3 } { 2 }23​ 
C)    23\sqrt [ 3 ] { 2 }32c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    23\frac { 2 } { 3 }32​

Question 7

For the given functions f and g, find the composition.
- f(x) =x2−6x+3;g(x) =xf ( x )  = x ^ { 2 } - 6 x + 3 ; g ( x )  = \sqrt { x } \quadf(x) =x2−6x+3;g(x) =x​  Find  (f∘g) (9) ( f \circ g )  ( 9 ) (f∘g) (9)

Accepted Answer

A)    −12- 12−12 
B)    −15- 15−15 
C)    −6- 6−6 
D)    −9- 9−9

Question 8

Solve the equation.
- log⁡9x2=4\log _ { 9 } x ^ { 2 } = 4log9​x2=4

Accepted Answer

A)   6561
B)   512
C)    81,−8181 , - 8181,−81 
D)    6,−66 , - 66,−6

Question 9

Use the power property to rewrite the expression.
- log⁡xyz\log _ { \mathrm { x } } \mathrm { y } ^ { \mathrm { z } }logx​yz

Accepted Answer

A)    zlog⁡yxz \log _ { y } xzlogy​x 
B)    ylog⁡xzy \log _ { x } zylogx​z 
C)    zlog⁡xyz \log _ { x } yzlogx​y 
D)    xlog⁡yzx \log _ { y } zxlogy​z

Question 10

Graph the function and its inverse on the same set of axes.
- f(x) =12x−4f ( x )  = \frac { 1 } { 2 } x - 4f(x) =21​x−4

Accepted Answer

A)  
B)  
C)  
D)

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

Simplify.
- log⁡2217\log _2 { 2 ^ { 17}}log2​217

Accepted Answer

A)   2
B)    log⁡217\log _ { 2 } 17log2​17 
C)   19
D)   17

Question 13

For the given functions f and g, find the requested function.
-If  f(x) =x2+4xf ( x )  = x ^ { 2 } + 4 xf(x) =x2+4x  and  g(x) =x+2g ( x )  = x + 2g(x) =x+2 , find  (g∘f) (2) ( g \circ f )  ( 2 ) (g∘f) (2)  .

Accepted Answer

A)   48
B)   16
C)   14
D)   32

Question 14

Solve. Round the answer to the nearest whole number.
-The size of the coyote population at a national park increases at the rate of  4.8%4.8 \%4.8%  per year. If the size of the current population is 149 , find how many coyotes there will be in 7 years.

Accepted Answer

A)   205 coyotes
B)   209 coyotes
C)   207 coyotes
D)   211 coyotes

Question 15

Graph the function.
- f(x) =log⁡x−2f(x) =\log x-2f(x) =logx−2

Accepted Answer

A)  
B)  
C)  
D)

Question 16

Use the following approximations to find the approximate value of the logarithmic expression: 
 log⁡b3≈0.5log⁡b8≈0.9\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9logb​3≈0.5logb​8≈0.9 
 log⁡b5≈0.7log⁡b20≈1.3\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3logb​5≈0.7logb​20≈1.3 
- log⁡b3\log _ { b } \sqrt { 3 }logb​3​  (Round answer to nearest hundredth.)

Accepted Answer

A)    0.710.710.71 
B)   1
C)    0.250.250.25 
D)    1.731.731.73

Question 17

Write the function F(x)  as a composition of f, g, or h.
- f(x) =x2−2g(x) =−6xh(x) =x+7F(x) =−6x+7\begin{array} { l } f ( x )  = x ^ { 2 } - 2 \quad g ( x )  = - 6 x \quad h ( x )  = \sqrt { x + 7 } \F ( x )  = \sqrt { - 6 x + 7 }\end{array}f(x) =x2−2g(x) =−6xh(x) =x+7​F(x) =−6x+7​​

Accepted Answer

A)    F(x) =(f∘h) (x) F ( x )  = ( f \circ h )  ( x ) F(x) =(f∘h) (x)  
B)    F(x) =(g∘h) (x) F ( x )  = ( g \circ h )  ( x ) F(x) =(g∘h) (x)  
C)    F(x) =(h∘f) (x) F ( x )  = ( h \circ f )  ( x ) F(x) =(h∘f) (x)  
D)    F(x) =(h∘g) (x) F ( x )  = ( h \circ g )  ( x ) F(x) =(h∘g) (x)

Question 18

Use a calculator to approximate the natural logarithm to four decimal places.
- ln⁡24\ln 24ln24

Accepted Answer

A)    0.31370.31370.3137 
B)    1.38021.38021.3802 
C)    8.85618.85618.8561 
D)    3.17813.17813.1781

Question 19

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

Accepted Answer

A)   one-to-one
B)   not one-to-one

Question 20

Graph the exponential function.
- f(x) =5x+1f(x) =5^{x}+1f(x) =5x+1

Accepted Answer

A)  
B)  
C)  
D)

Exam 12: Exponential and Logarithmic Functions

Determine whether the functions f and g are inverses of each other. - f(x)=x3+2;g(x)=x−23f ( x ) = x ^ { 3 } + 2 ; g ( x ) = \sqrt [ 3 ] { x - 2 }f(x)=x3+2;g(x)=3x−2​

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Write the function F(x) as a composition of f, g, or h. - f(x) =x2−2g(x) =−6xh(x) =x+7F(x) =−6x+7\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x + 7 } \\F ( x ) = \sqrt { - 6 x + 7 }\end{array}f(x) =x2−2g(x) =−6xh(x) =x+7​F(x) =−6x+7​​

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Use the power property to rewrite the expression. - log⁡xyz\log _ { \mathrm { x } } \mathrm { y } ^ { \mathrm { z } }logx​yz

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Solve the equation. - 5x=1255 ^ { x } = 1255x=125

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Simplify. - log⁡2217\log _2 { 2 ^ { 17}}log2​217

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Solve for x. - log⁡3x=2\log _ { 3 } x = 2log3​x=2

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Given the values of f and g, find the function value. - f(19) =14;g(19) =5f ( 19 ) = 14 ; g ( 19 ) = 5 \quadf(19) =14;g(19) =5 Find (f−g) (19) ( f - g ) ( 19 ) (f−g) (19)

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For the given functions f and g, find the composition. - f(x) =4x+5;g(x) =2x−1f ( x ) = 4 x + 5 ; g ( x ) = 2 x - 1 \quadf(x) =4x+5;g(x) =2x−1 Find (f∘g) (x) ( f \circ g ) ( x ) (f∘g) (x)

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For the given functions f and g, find the requested function. -If f(x) =x2+4xf ( x ) = x ^ { 2 } + 4 xf(x) =x2+4x and g(x) =x+2g ( x ) = x + 2g(x) =x+2 , find (g∘f) (2) ( g \circ f ) ( 2 ) (g∘f) (2) .

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Graph the function. - f(x) =log⁡x−2f(x) =\log x-2f(x) =logx−2

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Solve. Round the answer to the nearest whole number. -The size of the coyote population at a national park increases at the rate of 4.8%4.8 \%4.8% per year. If the size of the current population is 149 , find how many coyotes there will be in 7 years.

Correct AnswerverifiedShow Answer

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

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Solve the equation. - log⁡9x2=4\log _ { 9 } x ^ { 2 } = 4log9​x2=4

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Solve the equation. - log⁡23+log⁡2x=1\log _ { 2 } 3 + \log _ { 2 } x = 1log2​3+log2​x=1

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Graph the function and its inverse on the same set of axes. - f(x) =12x−4f ( x ) = \frac { 1 } { 2 } x - 4f(x) =21​x−4

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Use a calculator to approximate the natural logarithm to four decimal places. - ln⁡24\ln 24ln24

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Graph the exponential function. - f(x) =5x+1f(x) =5^{x}+1f(x) =5x+1

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

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For the given functions f and g, find the composition. - f(x) =x2−6x+3;g(x) =xf ( x ) = x ^ { 2 } - 6 x + 3 ; g ( x ) = \sqrt { x } \quadf(x) =x2−6x+3;g(x) =x​ Find (f∘g) (9) ( f \circ g ) ( 9 ) (f∘g) (9)

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Determine whether the functions f and g are inverses of each other. - $f ( x ) = x ^ { 3 } + 2 ; g ( x ) = \sqrt [ 3 ] { x - 2 }$

Correct Answer
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Write the function F(x) as a composition of f, g, or h. - $\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x + 7 } \\F ( x ) = \sqrt { - 6 x + 7 }\end{array}$

Correct Answer
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Use the power property to rewrite the expression. - $\log _ { \mathrm { x } } \mathrm { y } ^ { \mathrm { z } }$

Correct Answer
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Solve the equation. - $5 ^ { x } = 125$

Correct Answer
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Simplify. - $\log _2 { 2 ^ { 17}}$

Correct Answer
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Solve for x. - $\log _ { 3 } x = 2$

Correct Answer
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Given the values of f and g, find the function value. - $f ( 19 ) = 14 ; g ( 19 ) = 5 \quad$ Find $( f - g ) ( 19 )$

Correct Answer
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For the given functions f and g, find the composition. - $f ( x ) = 4 x + 5 ; g ( x ) = 2 x - 1 \quad$ Find $( f \circ g ) ( x )$

Correct Answer
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For the given functions f and g, find the requested function. -If $f ( x ) = x ^ { 2 } + 4 x$ and $g ( x ) = x + 2$ , find $( g \circ f ) ( 2 )$ .

Correct Answer
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Graph the function. - $f(x) =\log x-2$ $Graph the function. - f(x) =\log x-2 A) B) C) D)$

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Solve. Round the answer to the nearest whole number. -The size of the coyote population at a national park increases at the rate of $4.8 \%$ per year. If the size of the current population is 149 , find how many coyotes there will be in 7 years.

Correct Answer
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Correct Answer
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Solve the equation. - $\log _ { 9 } x ^ { 2 } = 4$

Correct Answer
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Solve the equation. - $\log _ { 2 } 3 + \log _ { 2 } x = 1$

Correct Answer
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Graph the function and its inverse on the same set of axes. - $f ( x ) = \frac { 1 } { 2 } x - 4$ $Graph the function and its inverse on the same set of axes. - f ( x ) = \frac { 1 } { 2 } x - 4 A) B) C) D)$

Correct Answer
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Correct Answer
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Use a calculator to approximate the natural logarithm to four decimal places. - $\ln 24$

Correct Answer
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Graph the exponential function. - $f(x) =5^{x}+1$ $Graph the exponential function. - f(x) =5^{x}+1 A) B) C) D)$

Correct Answer
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Correct Answer
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For the given functions f and g, find the composition. - $f ( x ) = x ^ { 2 } - 6 x + 3 ; g ( x ) = \sqrt { x } \quad$ Find $( f \circ g ) ( 9 )$

Correct Answer
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