Question 1

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

Accepted Answer

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

Question 2

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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 
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 8

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

Accepted Answer

A)  $8 + \log _ { 7 } x + \log _ { 3 } y$ 
B)  $3 \log _ { 7 } x + 5 \log _ { 7 } y$ 
C)  $15 \log _ { 7 } x + \log _ { 7 } y$ 
D)  $3 \log _ { 7 } x - 5 \log _ { 7 } y$ 
A)  $8 + \log _ { 7 } x + \log _ { 3 } y$ 
B)  $3 \log _ { 7 } x + 5 \log _ { 7 } y$ 
C)  $15 \log _ { 7 } x + \log _ { 7 } y$ 
D)  $3 \log _ { 7 } x - 5 \log _ { 7 } y$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

A)  $4.4$ 
B)  $1.6$ 
C)  $425.7$ 
D)  $359.5$ 
A)  $4.4$ 
B)  $1.6$ 
C)  $425.7$ 
D)  $359.5$

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 13

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

Accepted Answer

A)  $20 x + 24$ 
B)  $20 x + 9$ 
C)  $20 x + 4$ 
D)  $20 x + 1$ 
A)  $20 x + 24$ 
B)  $20 x + 9$ 
C)  $20 x + 4$ 
D)  $20 x + 1$

Question 14

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

Accepted Answer

A)  $\frac { 1 } { 4 } \log _ { 2 } \sqrt [ 4 ] { y }$ 
B)  $4 \log _ { 2 } y$ 
C)  $\frac { 1 } { 2 } \log _ { 4 } y$ 
D)  $\frac { 1 } { 4 } \log _ { 2 } \mathrm { y }$ 
A)  $\frac { 1 } { 4 } \log _ { 2 } \sqrt [ 4 ] { y }$ 
B)  $4 \log _ { 2 } y$ 
C)  $\frac { 1 } { 2 } \log _ { 4 } y$ 
D)  $\frac { 1 } { 4 } \log _ { 2 } \mathrm { y }$

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

A)  $\left\{ \frac { 15 } { 2 } \right\}$ 
B)  $\{ 4 \}$ 
C)  $\left\{ \frac { 2 } { 15 } \right\}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$ 
A)  $\left\{ \frac { 15 } { 2 } \right\}$ 
B)  $\{ 4 \}$ 
C)  $\left\{ \frac { 2 } { 15 } \right\}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 20

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

Accepted Answer

A)  $\left\{ \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ \frac { 27 } { 125 } \right\}$ 
C)  $\left\{ \frac { 27 } { 5 } \right\}$ 
D)  $\left\{ 3 ^ { 3 / 5 } \right\}$ 
A)  $\left\{ \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ \frac { 27 } { 125 } \right\}$ 
C)  $\left\{ \frac { 27 } { 5 } \right\}$ 
D)  $\left\{ 3 ^ { 3 / 5 } \right\}$

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

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

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 12,000 12\% 11

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

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

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)}

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

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

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 400 8 52

Write the function F(x) as a composition of f, g, or h. - f(x)=-1g(x)=-4xh(x)= F(x)=

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

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

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

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

Write the function F(x) as a composition of f, g, or h. - f(x)=-2g(x)=3xh(x)= F(x)=3-6

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

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

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

Real Numbers and Algebraic Expressions

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Exam 9: Exponential and Logarithmic Functions

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) .