Question 1

Graph the inverse of the function on the same set of axes.
-

Accepted Answer

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

Question 2

Graph the exponential function.
-$y = \left( \frac { 1 } { 3 } \right) ^ { x } - 1$

Accepted Answer

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

Question 3

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural } \quad \text { half-life } & \text { horizontal }
\end{array}$$
-The ______of functions $\mathrm { f }$ and $g$ is $( f \circ g ) ( x ) = f ( g ( x ) )$.

Accepted Answer

A)  logarithmic 
B)  inverse 
C)  composition 
D)  exponential 
A)  logarithmic 
B)  inverse 
C)  composition 
D)  exponential

Question 4

Provide an appropriate response.
-$\text { Graph } y = \left( \frac { 1 } { 4 } \right) ^ { x } + 2$

Accepted Answer

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

Question 5

Determine whether the function is a one-to-one function.
-$\mathrm { f } = \{ ( 6 , - 1 ) , ( - 4,0 ) , ( - 6,1 ) , ( - 8,2 ) \}$

Accepted Answer

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

Question 6

Graph the function.
-$f(x)=e^{3 x}$

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Solve the equation for x. Give an exact solution.
-$\ln 17 x = - 3$

Accepted Answer

A) $e ^ { - \frac { 3 } { 17 } }$ 
B)  $\frac { e ^ { - 3 } } { 17 }$ 
C)  $\frac { e ^ { 17 } } { - 3 }$ 
D)  $- 51$ 
A) $e ^ { - \frac { 3 } { 17 } }$ 
B)  $\frac { e ^ { - 3 } } { 17 }$ 
C)  $\frac { e ^ { 17 } } { - 3 }$ 
D)  $- 51$

Question 9

For the given functions f and g, find the requested function.
-$f ( x ) = 8 x ^ { 3 } ; g ( x ) = 3 x ^ { 2 } \quad$ Find $( f \cdot g ) ( x )$.

Accepted Answer

A)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 24 \mathrm { x } ^ { 5 }$ 
B)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = - 24 \mathrm { x } ^ { 5 }$ 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = - 24 \mathrm { x } ^ { 6 }$ 
D)  $( f \cdot g ) ( x ) = 24 x ^ { 6 }$ 
A)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 24 \mathrm { x } ^ { 5 }$ 
B)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = - 24 \mathrm { x } ^ { 5 }$ 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = - 24 \mathrm { x } ^ { 6 }$ 
D)  $( f \cdot g ) ( x ) = 24 x ^ { 6 }$

Question 10

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x).
-$h ( x ) = \sqrt [ 3 ] { x + 8 }$

Accepted Answer

A)  $f ( x ) = \sqrt { x } ; g ( x ) = x + 8$ 
B)  $f ( x ) = x ^ { 3 } ; g ( x ) = x + 8$ 
C)  $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = x + 8$ 
D)  $f ( x ) = x + 8 ; g ( x ) = \sqrt [ 3 ] { x }$ 
A)  $f ( x ) = \sqrt { x } ; g ( x ) = x + 8$ 
B)  $f ( x ) = x ^ { 3 } ; g ( x ) = x + 8$ 
C)  $f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = x + 8$ 
D)  $f ( x ) = x + 8 ; g ( x ) = \sqrt [ 3 ] { x }$

Question 11

Solve the equation.
-$4 ^ { x } = \frac { 1 } { 64 }$

Accepted Answer

A)  3 
B)  $\frac { 1 } { 16 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $- 3$ 
A)  3 
B)  $\frac { 1 } { 16 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $- 3$

Question 12

Write as a logarithmic equation.
-$19 ^ { 1 / 7 } = \sqrt [ 7 ] { 19 }$

Accepted Answer

A)  $\log _ { 1 / 7 } \sqrt [ 7 ] { 19 } = 19$ 
B)  $\log _ { 19 } \frac { 1 } { 7 } = \sqrt [ 7 ] { 19 }$ 
C)  $\log _ { 1 / 7 } 19 = \sqrt [ 7 ] { 19 }$ 
D)  $\log _ { 19 } \sqrt [ 7 ] { 19 } = \frac { 1 } { 7 }$ 
A)  $\log _ { 1 / 7 } \sqrt [ 7 ] { 19 } = 19$ 
B)  $\log _ { 19 } \frac { 1 } { 7 } = \sqrt [ 7 ] { 19 }$ 
C)  $\log _ { 1 / 7 } 19 = \sqrt [ 7 ] { 19 }$ 
D)  $\log _ { 19 } \sqrt [ 7 ] { 19 } = \frac { 1 } { 7 }$

Question 13

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-

Accepted Answer

A)  $12.5$ 
B)  $35.4$ 
C)  $112.5$ 
D)  $0.4$ 
A)  $12.5$ 
B)  $35.4$ 
C)  $112.5$ 
D)  $0.4$

Question 14

Provide an appropriate response.
-Solve $\ln ( 7 x + 1 ) = 1.56$ accurate to four decimal places.

Accepted Answer

A)  $0.2501$ 
B)  $0.5370$ 
C)  $1.0833$ 
D)  $0.8227$ 
A)  $0.2501$ 
B)  $0.5370$ 
C)  $1.0833$ 
D)  $0.8227$

Question 15

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-$f = \{ ( - 9 , - 8 ) , ( 8,9 ) , ( 2,1 ) , ( - 2 , - 1 ) \}$

Accepted Answer

A)  not one-to-one 
B)  $f ^ { - 1 } = \{ ( - 8 , - 9 ) , ( 9,8 ) , ( 1,2 ) , ( - 1 , - 2 ) \}$ 
C)  $f ^ { - 1 } = \{ ( - 1,2 ) , ( 9,8 ) , ( - 8,8 ) , ( 1 , - 2 ) \}$ 
D)  $f ^ { - 1 } = \{ ( - 1,2 ) , ( 2,8 ) , ( - 8 , - 9 ) , ( 1 , - 2 ) \}$ 
A)  not one-to-one 
B)  $f ^ { - 1 } = \{ ( - 8 , - 9 ) , ( 9,8 ) , ( 1,2 ) , ( - 1 , - 2 ) \}$ 
C)  $f ^ { - 1 } = \{ ( - 1,2 ) , ( 9,8 ) , ( - 8,8 ) , ( 1 , - 2 ) \}$ 
D)  $f ^ { - 1 } = \{ ( - 1,2 ) , ( 2,8 ) , ( - 8 , - 9 ) , ( 1 , - 2 ) \}$

Question 16

Use a calculator to approximate the natural logarithm to four decimal places.
-In $0.983$

Accepted Answer

A)  $- 0.0171$ 
B)  $0.0171$ 
C)  $0.0074$ 
D)  $- 0.0074$ 
A)  $- 0.0171$ 
B)  $0.0171$ 
C)  $0.0074$ 
D)  $- 0.0074$

Question 17

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

Accepted Answer

A)  2638 
B)  2277 
C)  3050 
D)  2594 
A)  2638 
B)  2277 
C)  3050 
D)  2594

Question 18

For the given functions f and g, find the composition.
-$f ( x ) = - 5 x + 8 ; g ( x ) = 3 x + 8 \quad$ Find $( g \circ f ) ( x )$

Accepted Answer

A)  $- 15 x + 48$ 
B)  $- 15 x + 32$ 
C)  $- 15 x - 16$ 
D)  $15 x + 32$ 
A)  $- 15 x + 48$ 
B)  $- 15 x + 32$ 
C)  $- 15 x - 16$ 
D)  $15 x + 32$

Question 19

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

Accepted Answer

A)  $\frac { 6 } { 5 }$ 
B)  $- 2$ 
C)  2 
D)  $\frac { 1 } { 3 }$ 
A)  $\frac { 6 } { 5 }$ 
B)  $- 2$ 
C)  2 
D)  $\frac { 1 } { 3 }$

Question 20

Graph the function and its inverse on the same set of axes.
-$f(x)=x^{3}+2$

Accepted Answer

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

Graph the inverse of the function on the same set of axes. -

Graph the exponential function. - $y = \left( \frac { 1 } { 3 } \right) ^ { x } - 1$ $Graph the exponential function. - y = \left( \frac { 1 } { 3 } \right) ^ { x } - 1$

Provide an appropriate response. - $\text { Graph } y = \left( \frac { 1 } { 4 } \right) ^ { x } + 2$ $Provide an appropriate response. - \text { Graph } y = \left( \frac { 1 } { 4 } \right) ^ { x } + 2$

Determine whether the function is a one-to-one function. - $\mathrm { f } = \{ ( 6 , - 1 ) , ( - 4,0 ) , ( - 6,1 ) , ( - 8,2 ) \}$

Graph the function. - $f(x)=e^{3 x}$ $Graph the function. - f(x)=e^{3 x}$

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

Solve the equation for x. Give an exact solution. - $\ln 17 x = - 3$

For the given functions f and g, find the requested function. - $f ( x ) = 8 x ^ { 3 } ; g ( x ) = 3 x ^ { 2 } \quad$ Find $( f \cdot g ) ( x )$ .

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - $h ( x ) = \sqrt [ 3 ] { x + 8 }$

Solve the equation. - $4 ^ { x } = \frac { 1 } { 64 }$

Write as a logarithmic equation. - $19 ^ { 1 / 7 } = \sqrt [ 7 ] { 19 }$

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. -

Provide an appropriate response. -Solve $\ln ( 7 x + 1 ) = 1.56$ accurate to four decimal places.

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $f = \{ ( - 9 , - 8 ) , ( 8,9 ) , ( 2,1 ) , ( - 2 , - 1 ) \}$

Use a calculator to approximate the natural logarithm to four decimal places. -In $0.983$

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

For the given functions f and g, find the composition. - $f ( x ) = - 5 x + 8 ; g ( x ) = 3 x + 8 \quad$ Find $( g \circ f ) ( x )$

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

Graph the function and its inverse on the same set of axes. - $f(x)=x^{3}+2$ $Graph the function and its inverse on the same set of axes. - f(x)=x^{3}+2$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Exponential and Logarithmic Functions

Graph the inverse of the function on the same set of axes. -

Graph the exponential function. - y=(13)x−1y = \left( \frac { 1 } { 3 } \right) ^ { x } - 1y=(31​)x−1

Provide an appropriate response. - Graph y=(14)x+2\text { Graph } y = \left( \frac { 1 } { 4 } \right) ^ { x } + 2 Graph y=(41​)x+2

Determine whether the function is a one-to-one function. - f={(6,−1),(−4,0),(−6,1),(−8,2)}\mathrm { f } = \{ ( 6 , - 1 ) , ( - 4,0 ) , ( - 6,1 ) , ( - 8,2 ) \}f={(6,−1),(−4,0),(−6,1),(−8,2)}

Graph the function. - f(x)=e3xf(x)=e^{3 x}f(x)=e3x

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

Solve the equation for x. Give an exact solution. - ln⁡17x=−3\ln 17 x = - 3ln17x=−3

For the given functions f and g, find the requested function. - f(x)=8x3;g(x)=3x2f ( x ) = 8 x ^ { 3 } ; g ( x ) = 3 x ^ { 2 } \quadf(x)=8x3;g(x)=3x2 Find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x) .

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - h(x)=x+83h ( x ) = \sqrt [ 3 ] { x + 8 }h(x)=3x+8​

Solve the equation. - 4x=1644 ^ { x } = \frac { 1 } { 64 }4x=641​

Write as a logarithmic equation. - 191/7=19719 ^ { 1 / 7 } = \sqrt [ 7 ] { 19 }191/7=719​

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. -

Provide an appropriate response. -Solve ln⁡(7x+1)=1.56\ln ( 7 x + 1 ) = 1.56ln(7x+1)=1.56 accurate to four decimal places.

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - f={(−9,−8),(8,9),(2,1),(−2,−1)}f = \{ ( - 9 , - 8 ) , ( 8,9 ) , ( 2,1 ) , ( - 2 , - 1 ) \}f={(−9,−8),(8,9),(2,1),(−2,−1)}

Use a calculator to approximate the natural logarithm to four decimal places. -In 0.9830.9830.983

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

For the given functions f and g, find the composition. - f(x)=−5x+8;g(x)=3x+8f ( x ) = - 5 x + 8 ; g ( x ) = 3 x + 8 \quadf(x)=−5x+8;g(x)=3x+8 Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Solve the equation. - log⁡(x+4)=log⁡(4x−2)\log ( x + 4 ) = \log ( 4 x - 2 )log(x+4)=log(4x−2)

Graph the function and its inverse on the same set of axes. - f(x)=x3+2f(x)=x^{3}+2f(x)=x3+2

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Graph the exponential function. - $y = \left( \frac { 1 } { 3 } \right) ^ { x } - 1$ $Graph the exponential function. - y = \left( \frac { 1 } { 3 } \right) ^ { x } - 1$

Provide an appropriate response. - $\text { Graph } y = \left( \frac { 1 } { 4 } \right) ^ { x } + 2$ $Provide an appropriate response. - \text { Graph } y = \left( \frac { 1 } { 4 } \right) ^ { x } + 2$

Determine whether the function is a one-to-one function. - $\mathrm { f } = \{ ( 6 , - 1 ) , ( - 4,0 ) , ( - 6,1 ) , ( - 8,2 ) \}$

Graph the function. - $f(x)=e^{3 x}$ $Graph the function. - f(x)=e^{3 x}$

Solve the equation for x. Give an exact solution. - $\ln 17 x = - 3$

For the given functions f and g, find the requested function. - $f ( x ) = 8 x ^ { 3 } ; g ( x ) = 3 x ^ { 2 } \quad$ Find $( f \cdot g ) ( x )$ .

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - $h ( x ) = \sqrt [ 3 ] { x + 8 }$

Solve the equation. - $4 ^ { x } = \frac { 1 } { 64 }$

Write as a logarithmic equation. - $19 ^ { 1 / 7 } = \sqrt [ 7 ] { 19 }$

Provide an appropriate response. -Solve $\ln ( 7 x + 1 ) = 1.56$ accurate to four decimal places.

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $f = \{ ( - 9 , - 8 ) , ( 8,9 ) , ( 2,1 ) , ( - 2 , - 1 ) \}$

Use a calculator to approximate the natural logarithm to four decimal places. -In $0.983$

For the given functions f and g, find the composition. - $f ( x ) = - 5 x + 8 ; g ( x ) = 3 x + 8 \quad$ Find $( g \circ f ) ( x )$

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

Graph the function and its inverse on the same set of axes. - $f(x)=x^{3}+2$ $Graph the function and its inverse on the same set of axes. - f(x)=x^{3}+2$