Question 1

Find the value of the logarithmic expression.
- log⁡553\log _ { 5 } 5 ^ { 3 }log5​53

Accepted Answer

A)   5
B)   3
C)   125
D)   25

Question 2

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-  Original  Half-Life  Amount  (in years)   Number  of Years  Final Amount after  x Time Intervals 400852\begin{array}{c|c|c|c}	ext { Original } & 	ext { Half-Life } \	ext { Amount } & 	ext { (in years)  } & \begin{array}{c}	ext { Number } \	ext { of Years }\end{array} & \begin{array}{c}	ext { Final Amount after } \	ext { x Time Intervals }\end{array} \\hline 400 & 8 & 52 &\end{array} Original  Amount 400​ Half-Life  (in years)  8​ Number  of Years ​52​ Final Amount after  x Time Intervals ​​​

Accepted Answer

A)    4.44.44.4 
B)    1.61.61.6 
C)    425.7425.7425.7 
D)    359.5359.5359.5

Question 3

Write the expression as sums or differences of multiples of logarithms.
- log⁡7x3y5\log _ { 7 } x ^ { 3 } y ^ { 5 }log7​x3y5

Accepted Answer

A)    8+log⁡7x+log⁡3y8 + \log _ { 7 } x + \log _ { 3 } y8+log7​x+log3​y 
B)    3log⁡7x+5log⁡7y3 \log _ { 7 } x + 5 \log _ { 7 } y3log7​x+5log7​y 
C)    15log⁡7x+log⁡7y15 \log _ { 7 } x + \log _ { 7 } y15log7​x+log7​y 
D)    3log⁡7x−5log⁡7y3 \log _ { 7 } x - 5 \log _ { 7 } y3log7​x−5log7​y

Question 4

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-f = {(-6, -9) , (6, 9) , (7, 11) , (-7, -11) }

Accepted Answer

A)   f-1 = {(-9, -6) , (9, 6) , (11, 6) , (-11, -7) }
B)   f-1 = {(-9, -6) , (-6, 6) , (11, 7) , (-11, -7) }
C)   f-1 = {(-9, -6) , (9, 6) , (11, 7) , (-11, -7) }
D)   not one-to-one

Question 5

Solve for x.
- log⁡3/5x=3\log _ { 3 / 5 } x = 3log3/5​x=3

Accepted Answer

A)    {35}\left\{ \frac { 3 } { 5 } \right\}{53​} 
B)    {27125}\left\{ \frac { 27 } { 125 } \right\}{12527​} 
C)    {275}\left\{ \frac { 27 } { 5 } \right\}{527​} 
D)    {33/5}\left\{ 3 ^ { 3 / 5 } \right\}{33/5}

Question 6

Write the function F(x)  as a composition of f, g, or h.
- f(x) =x2−2g(x) =3xh(x) =x−8F(x) =3x2−6\begin{array} { l } f ( x )  = x ^ { 2 } - 2 \quad g ( x )  = 3 x \quad h ( x )  = \sqrt { x - 8 } \F ( x )  = 3 x ^ { 2 } - 6\end{array}f(x) =x2−2g(x) =3xh(x) =x−8​F(x) =3x2−6​

Accepted Answer

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

Question 7

Use the exponential growth formula to find the final amount. Round to the nearest whole.
-

Accepted Answer

A)   802,831
B)    2,025,6872,025,6872,025,687 
C)    1,027,3351,027,3351,027,335 
D)   908,555

Question 8

Solve the equation.
- log⁡4(x+2) −log⁡4x=2\log _ { 4 } ( x + 2 )  - \log _ { 4 } x = 2log4​(x+2) −log4​x=2

Accepted Answer

A)    {152}\left\{ \frac { 15 } { 2 } \right\}{215​} 
B)    {4}\{ 4 \}{4} 
C)    {215}\left\{ \frac { 2 } { 15 } \right\}{152​} 
D)    {18}\left\{ \frac { 1 } { 8 } \right\}{81​}

Question 9

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

Accepted Answer

A)    20x+2420 x + 2420x+24 
B)    20x+920 x + 920x+9 
C)    20x+420 x + 420x+4 
D)    20x+120 x + 120x+1

Question 10

Solve.
-Business people are concerned with cost functions, revenue functions, and profit functions. Suppose the revenue  R(x) R ( x ) R(x)   for  xxx  units of a product can be described by  R(x) =410xR ( x )  = 410 xR(x) =410x , and the cost  C(x) C ( x ) C(x)   can be described by  C(x) C ( x ) C(x)    =2900+110x= 2900 + 110 x=2900+110x . Find the profit  P(x) P ( x ) P(x)   for  xxx  units.

Accepted Answer

A)    P(x) =300x−2900P ( x )  = \frac { 300 } { x } - 2900P(x) =x300​−2900 
B)    P(x) =300x+2900\mathrm { P } ( \mathrm { x } )  = 300 \mathrm { x } + 2900P(x) =300x+2900 
C)    P(x) =300x−2900P ( x )  = 300 x - 2900P(x) =300x−2900 
D)    P(x) =520x−2900P ( x )  = 520 x - 2900P(x) =520x−2900

Question 11

Use the exponential decay formula to find the final amount. Round to the nearest whole.
-  Original  Amount  Decay  Rate per Year  Number  of Years,  Final Amount after  x Years of Decay 12,00012%11\begin{array}{c|c|c|c}\begin{array}{c}	ext { Original } \	ext { Amount }\end{array} & \begin{array}{c}	ext { Decay } \	ext { Rate per Year }\end{array} & \begin{array}{c}	ext { Number } \	ext { of Years, }\end{array} & \begin{array}{c}	ext { Final Amount after } \	ext { x Years of Decay }\end{array} \\hline 12,000 & 12 \% & 11 &\end{array} Original  Amount ​12,000​ Decay  Rate per Year ​12%​ Number  of Years, ​11​ Final Amount after  x Years of Decay ​​​

Accepted Answer

A)   2594
B)   3330
C)   2964
D)   2941

Question 12

Provide an appropriate response.
-If  f(x) =xf ( x )  = xf(x) =x  and  g(x) =2x−7g ( x )  = 2 x - 7g(x) =2x−7 , find  (f⋅g) (x) ( f \cdot g )  ( x ) (f⋅g) (x)  .

Accepted Answer

A)    2x2−7x2 x ^ { 2 } - 7 x2x2−7x 
B)    2x−72 x - 72x−7 
C)    3x−73 x - 73x−7 
D)    2x2−72 x ^ { 2 } - 72x2−7

Question 13

Determine whether the functions f and g are inverses of each other.
- f(x) =(x+2) 3−3;g(x) =x+33+2f ( x )  = ( x + 2 )  ^ { 3 } - 3 ; g ( x )  = \sqrt [ 3 ] { x + 3 } + 2f(x) =(x+2) 3−3;g(x) =3x+3​+2

Accepted Answer

A)   Yes
B)    No\mathrm { No }No

Question 14

Write the function F(x)  as a composition of f, g, or h.
- f(x) =x2−1g(x) =−4xh(x) =x−2F(x) =x2−3\begin{array} { l } f ( x )  = x ^ { 2 } - 1 \quad g ( x )  = - 4 x \quad h ( x )  = \sqrt { x - 2 } \F ( x )  = \sqrt { x ^ { 2 } - 3 }\end{array}f(x) =x2−1g(x) =−4xh(x) =x−2​F(x) =x2−3​​

Accepted Answer

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

Question 15

Solve the equation for x. Give an approximate solution accurate to four decimal places.
- log⁡(3x+7) =−0.7\log ( 3 x + 7 )  = - 0.7log(3x+7) =−0.7

Accepted Answer

A)    {−0.9715}\{ - 0.9715 \}{−0.9715} 
B)    {−20.4015}\{ - 20.4015 \}{−20.4015} 
C)    {−6.8005}\{ - 6.8005 \}{−6.8005} 
D)    {−2.2668}\{ - 2.2668 \}{−2.2668}

Question 16

Use the exponential decay formula to find the final amount. Round to the nearest whole.
-

Accepted Answer

A)   15
B)   10
C)   21
D)   28

Question 17

Use the power property to rewrite the expression.
- log⁡2y4\log _ { 2 } \sqrt [ 4 ] { y }log2​4y​

Accepted Answer

A)    14log⁡2y4\frac { 1 } { 4 } \log _ { 2 } \sqrt [ 4 ] { y }41​log2​4yc-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'/>​ 
B)    4log⁡2y4 \log _ { 2 } y4log2​y 
C)    12log⁡4y\frac { 1 } { 2 } \log _ { 4 } y21​log4​y 
D)    14log⁡2y\frac { 1 } { 4 } \log _ { 2 } \mathrm { y }41​log2​y

Question 18

Graph the exponential function.
- f(x) =(12) x+1f(x) =\left(\frac{1}{2}\right) ^{x+1}f(x) =(21​) x+1

Accepted Answer

A)  
B)  
C)  
D)

Question 19

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

Accepted Answer

A)   Yes
B)   No

Question 20

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once.   inverse  common  composition symmetric  exponential  vertical  logarithmic  natural half-life  horizontal \begin{array} { l l l l } 	ext { inverse } & 	ext { common } & 	ext { composition symmetric } & 	ext { exponential } \	ext { vertical } & 	ext { logarithmic } & 	ext { natural half-life } & 	ext { horizontal }\end{array} inverse  vertical ​ common  logarithmic ​ composition symmetric  natural half-life ​ exponential  horizontal ​ 
-The graphs of  f\mathrm { f }f  and  f−1\mathrm { f } ^ { - 1 }f−1  are ــــــــــــabout the line  y=xy = xy=x .

Accepted Answer

A)   horizontal
B)   inverse
C)   symmetric
D)   vertical

Exam 9: Exponential and Logarithmic Functions

Correct Answer
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Write the expression as sums or differences of multiples of logarithms. - $\log _ { 7 } x ^ { 3 } y ^ { 5 }$

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

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

Correct Answer
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Provide an appropriate response. -If $f ( x ) = x$ and $g ( x ) = 2 x - 7$ , find $( f \cdot g ) ( x )$ .

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Use the power property to rewrite the expression. - $\log _ { 2 } \sqrt [ 4 ] { y }$

Correct Answer
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Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Correct Answer
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Write the function F(x) as a composition of f, g, or h. - $\begin{array} { l } f ( x ) = x ^ { 2 } - 1 \quad g ( x ) = - 4 x \quad h ( x ) = \sqrt { x - 2 } \\F ( x ) = \sqrt { x ^ { 2 } - 3 }\end{array}$

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Use the exponential decay formula to find the final amount. Round to the nearest whole. -

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Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log ( 3 x + 7 ) = - 0.7$

Correct Answer
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If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. -f = {(-6, -9) , (6, 9) , (7, 11) , (-7, -11) }

Correct Answer
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Solve for x. - $\log _ { 3 / 5 } x = 3$

Correct Answer
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Write the function F(x) as a composition of f, g, or h. - $\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 8 } \\F ( x ) = 3 x ^ { 2 } - 6\end{array}$

Correct Answer
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Find the value of the logarithmic expression. - $\log _ { 5 } 5 ^ { 3 }$

Correct Answer
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Solve the equation. - $\log _ { 4 } ( x + 2 ) - \log _ { 4 } x = 2$

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Graph the exponential function. - $f(x) =\left(\frac{1}{2}\right) ^{x+1}$ $Graph the exponential function. - f(x) =\left(\frac{1}{2}\right) ^{x+1} A) B) C) D)$

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

Correct Answer
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Exam 9: Exponential and Logarithmic Functions

Correct AnswerverifiedShow Answer

Write the expression as sums or differences of multiples of logarithms. - log⁡7x3y5\log _ { 7 } x ^ { 3 } y ^ { 5 }log7​x3y5

Correct AnswerverifiedShow Answer

Determine whether the functions f and g are inverses of each other. - f(x) =(x+2) 3−3;g(x) =x+33+2f ( x ) = ( x + 2 ) ^ { 3 } - 3 ; g ( x ) = \sqrt [ 3 ] { x + 3 } + 2f(x) =(x+2) 3−3;g(x) =3x+3​+2

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Provide an appropriate response. -If f(x) =xf ( x ) = xf(x) =x and g(x) =2x−7g ( x ) = 2 x - 7g(x) =2x−7 , find (f⋅g) (x) ( f \cdot g ) ( x ) (f⋅g) (x) .

Correct AnswerverifiedShow Answer

Use the power property to rewrite the expression. - log⁡2y4\log _ { 2 } \sqrt [ 4 ] { y }log2​4y​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Use the exponential decay formula to find the final amount. Round to the nearest whole. -

Correct AnswerverifiedShow Answer

Solve the equation for x. Give an approximate solution accurate to four decimal places. - log⁡(3x+7) =−0.7\log ( 3 x + 7 ) = - 0.7log(3x+7) =−0.7

Correct AnswerverifiedShow Answer

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. -f = {(-6, -9) , (6, 9) , (7, 11) , (-7, -11) }

Correct AnswerverifiedShow Answer

Solve for x. - log⁡3/5x=3\log _ { 3 / 5 } x = 3log3/5​x=3

Correct AnswerverifiedShow Answer

Write the function F(x) as a composition of f, g, or h. - f(x) =x2−2g(x) =3xh(x) =x−8F(x) =3x2−6\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 8 } \\F ( x ) = 3 x ^ { 2 } - 6\end{array}f(x) =x2−2g(x) =3xh(x) =x−8​F(x) =3x2−6​

Correct AnswerverifiedShow Answer

Find the value of the logarithmic expression. - log⁡553\log _ { 5 } 5 ^ { 3 }log5​53

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the equation. - log⁡4(x+2) −log⁡4x=2\log _ { 4 } ( x + 2 ) - \log _ { 4 } x = 2log4​(x+2) −log4​x=2

Correct AnswerverifiedShow Answer

Graph the exponential function. - f(x) =(12) x+1f(x) =\left(\frac{1}{2}\right) ^{x+1}f(x) =(21​) x+1

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Correct Answer
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Write the expression as sums or differences of multiples of logarithms. - $\log _ { 7 } x ^ { 3 } y ^ { 5 }$

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

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Provide an appropriate response. -If $f ( x ) = x$ and $g ( x ) = 2 x - 7$ , find $( f \cdot g ) ( x )$ .

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Use the power property to rewrite the expression. - $\log _ { 2 } \sqrt [ 4 ] { y }$

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Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log ( 3 x + 7 ) = - 0.7$

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Solve for x. - $\log _ { 3 / 5 } x = 3$

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Write the function F(x) as a composition of f, g, or h. - $\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = 3 x \quad h ( x ) = \sqrt { x - 8 } \\F ( x ) = 3 x ^ { 2 } - 6\end{array}$

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Find the value of the logarithmic expression. - $\log _ { 5 } 5 ^ { 3 }$

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Solve the equation. - $\log _ { 4 } ( x + 2 ) - \log _ { 4 } x = 2$

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Graph the exponential function. - $f(x) =\left(\frac{1}{2}\right) ^{x+1}$ $Graph the exponential function. - f(x) =\left(\frac{1}{2}\right) ^{x+1} A) B) C) D)$

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

Correct Answer
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