Question 1

Solve the equation. Round to the nearest thousandth.
-$168 ( 1.31 ) ^ { x / 2 } = 336$

Accepted Answer

A)  $\{ 6.444 \}$ 
B)  $\{ 3.824 \}$ 
C)  $\{ 5.134 \}$ 
D)  $\{ 0.779 \}$ 
A)  $\{ 6.444 \}$ 
B)  $\{ 3.824 \}$ 
C)  $\{ 5.134 \}$ 
D)  $\{ 0.779 \}$

Question 2

Solve the equation.
-$$\left( \frac { 3 } { 7 } \right) ^ { x } = \frac { 2401 } { 81 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 4 } \right\}$ 
B)  $\{ - 4 \}$ 
C)  $\left\{ - \frac { 1 } { 4 } \right\}$ 
D)  $\{ 4 \}$ 
A)  $\left\{ \frac { 1 } { 4 } \right\}$ 
B)  $\{ - 4 \}$ 
C)  $\left\{ - \frac { 1 } { 4 } \right\}$ 
D)  $\{ 4 \}$

Question 3

Write the word or phrase that best completes each statement or answers the question.
-Without solving the inequality, what are the restrictions on $x$ if $\log _ { 2 } ( x - 3 ) - \log _ { 2 } ( x + 5 ) \leq$ 4? Explain.

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

The graph of a function f is given. Use the graph to find the indicated value.
-$f ^ { - 1 } ( 3 )$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $- 4$ 
C)  $- \frac { 5 } { 2 }$ 
D)  1 
A)  $- \frac { 1 } { 2 }$ 
B)  $- 4$ 
C)  $- \frac { 5 } { 2 }$ 
D)  1

Question 5

Graph the function.
-$f(x)=\left(\frac{3}{5}\right)^{x}$

Accepted Answer

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

Question 6

Write the word or phrase that best completes each statement or answers the question.
-Use the formula $\mathrm { D } = 10.0 \log \left( \mathrm { S } / \mathrm { S } _ { 0 } \right)$, where the loudness of a sound in decibels is determined by $\mathrm { S }$, the number of watt $/ \mathrm { m } ^ { 2 }$ produced by the soundwave, and $\mathrm { S } _ { 0 } = 1.00 \times 10 ^ { - 12 } \mathrm { watt } / \mathrm { m } ^ { 2 }$. A certain noise produces $2.54 \times 10 ^ { - 4 } \mathrm { watt } / \mathrm { m } ^ { 2 }$ of power. What is the decibel level of this noise? (Round to the nearest unit.)

Accepted Answer

A)  8 decibels 
B)  74 decibels 
C)  194 decibels 
D)  84 decibels 
A)  8 decibels 
B)  74 decibels 
C)  194 decibels 
D)  84 decibels

Question 7

Write the word or phrase that best completes each statement or answers the question.
-How long will it take for prices in the economy to double at a $12 \%$ annual inflation rate?

Accepted Answer

A)  $6.12 \mathrm { yr }$ 
B)  $5.67 \mathrm { yr }$ 
C)  $9.69 \mathrm { yr }$ 
D)  $23.45 \mathrm { yr }$ 
A)  $6.12 \mathrm { yr }$ 
B)  $5.67 \mathrm { yr }$ 
C)  $9.69 \mathrm { yr }$ 
D)  $23.45 \mathrm { yr }$

Question 8

Graph the exponential function using transformations where appropriate.
-$f(x)=3^{x-3}-1$

Accepted Answer

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

Question 9

Evaluate the logarithm.
-$\log _ { 8 } 512$

Accepted Answer

A)  8 
B)  512 
C)  24 
D)  3 
A)  8 
B)  512 
C)  24 
D)  3

Question 10

Write an equivalent expression in exponential form.
-$\log _ { 2 } 16 = 4$

Accepted Answer

A)  $2 ^ { 4 } = 16$ 
B)  $4 ^ { 2 } = 16$ 
C)  $16 ^ { 4 } = 2$ 
D)  $216 = 4$ 
A)  $2 ^ { 4 } = 16$ 
B)  $4 ^ { 2 } = 16$ 
C)  $16 ^ { 4 } = 2$ 
D)  $216 = 4$

Question 11

Solve the problem.
-Let f(x) compute the cost of a rental car after x days of use at $40 per day. What does f-1(x) compute?

Accepted Answer

A)  The cost of rental for 40 days 
B)  The number of days rented for 40 dollars 
C)  The cost of rental for x days 
D)  The number of days rented for x dollars 
A)  The cost of rental for 40 days 
B)  The number of days rented for 40 dollars 
C)  The cost of rental for x days 
D)  The number of days rented for x dollars

Question 12

Decide whether the given functions are inverses.
-

Accepted Answer

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

Question 13

Solve the equation and express the solution in exact form.
-$\log _ { 4 } ( x - 5 ) + \log _ { 4 } ( x - 5 ) = 1$

Accepted Answer

A)  $\{ - \sqrt { 26 } , \sqrt { 26 } \}$ 
B)  $\{ 7 \}$ 
C)  $\{ \sqrt { 26 } \}$ 
D)  $\{ - 7,7 \}$ 
A)  $\{ - \sqrt { 26 } , \sqrt { 26 } \}$ 
B)  $\{ 7 \}$ 
C)  $\{ \sqrt { 26 } \}$ 
D)  $\{ - 7,7 \}$

Question 14

Provide an appropriate response.
-The graph of an exponential function with base a is given. Sketch the graph of h(x) = a-x.
Give the domain and range of h. $f(x)=a^{X}$

Accepted Answer

The answer of Provide an appropriate response.
-The graph of an...

Question 15

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$f ( x ) = ( x + 8 ) ^ { 2 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 8 }$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } - 8$ 
C)  not a one-to-one 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x - 8 } }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 8 }$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } - 8$ 
C)  not a one-to-one 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x - 8 } }$

Question 16

For the function as defined that is one-to-one, graph f and f-1 on the same axes.
-$$f ( x ) = \frac { 5 } { x }$$

Accepted Answer

A) $\text { Function is its own inverse }$
  
B) 
  
C) 
  
D)  Function is its own inverse
  
A) $\text { Function is its own inverse }$
  
B) 
  
C) 
  
D)  Function is its own inverse

Question 17

For the function as defined that is one-to-one, graph f and f-1 on the same axes.
-$$f ( x ) = 4 x$$

Accepted Answer

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

Question 18

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses.
-$$f ( x ) = \frac { 2 + x } { x } , \quad g ( x ) = \frac { 2 } { x - 1 }$$

Accepted Answer

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

Question 19

Graph the function. Give the domain and range.
-$f(x)=\log _{1 / 3}(x+2)$

Accepted Answer

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

Question 20

An everyday activity is described. Keeping in mind that an inverse operation ʺundoesʺ what an operation does, describe each inverse activity.
-opening a door

Accepted Answer

A)  opening the window 
B)  closing the door 
C)  locking the door 
D)  going out of the door 
A)  opening the window 
B)  closing the door 
C)  locking the door 
D)  going out of the door

Solve the equation. Round to the nearest thousandth. - $168 ( 1.31 ) ^ { x / 2 } = 336$

Solve the equation. - $\left( \frac { 3 } { 7 } \right) ^ { x } = \frac { 2401 } { 81 }$

Write the word or phrase that best completes each statement or answers the question. -Without solving the inequality, what are the restrictions on $x$ if $\log _ { 2 } ( x - 3 ) - \log _ { 2 } ( x + 5 ) \leq$ 4? Explain.

The graph of a function f is given. Use the graph to find the indicated value. - $f ^ { - 1 } ( 3 )$ $The graph of a function f is given. Use the graph to find the indicated value. - f ^ { - 1 } ( 3 )$

Graph the function. - $f(x)=\left(\frac{3}{5}\right)^{x}$ $Graph the function. - f(x)=\left(\frac{3}{5}\right)^{x}$

Write the word or phrase that best completes each statement or answers the question. -How long will it take for prices in the economy to double at a $12 \%$ annual inflation rate?

Graph the exponential function using transformations where appropriate. - $f(x)=3^{x-3}-1$ $Graph the exponential function using transformations where appropriate. - f(x)=3^{x-3}-1$

Evaluate the logarithm. - $\log _ { 8 } 512$

Write an equivalent expression in exponential form. - $\log _ { 2 } 16 = 4$

Solve the problem. -Let f(x) compute the cost of a rental car after x days of use at $40 per day. What does f-1(x) compute?

Decide whether the given functions are inverses. -

Solve the equation and express the solution in exact form. - $\log _ { 4 } ( x - 5 ) + \log _ { 4 } ( x - 5 ) = 1$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = ( x + 8 ) ^ { 2 }$

For the function as defined that is one-to-one, graph f and f-1 on the same axes. - $f ( x ) = \frac { 5 } { x }$ $For the function as defined that is one-to-one, graph f and f-1 on the same axes. - f ( x ) = \frac { 5 } { x }$

For the function as defined that is one-to-one, graph f and f-1 on the same axes. - $f ( x ) = 4 x$

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = \frac { 2 + x } { x } , \quad g ( x ) = \frac { 2 } { x - 1 }$

Graph the function. Give the domain and range. - $f(x)=\log _{1 / 3}(x+2)$ $Graph the function. Give the domain and range. - f(x)=\log _{1 / 3}(x+2)$

An everyday activity is described. Keeping in mind that an inverse operation ʺundoesʺ what an operation does, describe each inverse activity. -opening a door

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 4: Inverse, Exponential, and Logarithmic Functions

Solve the equation. Round to the nearest thousandth. - 168(1.31)x/2=336168 ( 1.31 ) ^ { x / 2 } = 336168(1.31)x/2=336

Solve the equation. - (37)x=240181\left( \frac { 3 } { 7 } \right) ^ { x } = \frac { 2401 } { 81 }(73​)x=812401​

Write the word or phrase that best completes each statement or answers the question. -Without solving the inequality, what are the restrictions on xxx if log⁡2(x−3)−log⁡2(x+5)≤\log _ { 2 } ( x - 3 ) - \log _ { 2 } ( x + 5 ) \leqlog2​(x−3)−log2​(x+5)≤ 4? Explain.

The graph of a function f is given. Use the graph to find the indicated value. - f−1(3)f ^ { - 1 } ( 3 )f−1(3)

Graph the function. - f(x)=(35)xf(x)=\left(\frac{3}{5}\right)^{x}f(x)=(53​)x

Write the word or phrase that best completes each statement or answers the question. -How long will it take for prices in the economy to double at a 12%12 \%12% annual inflation rate?

Graph the exponential function using transformations where appropriate. - f(x)=3x−3−1f(x)=3^{x-3}-1f(x)=3x−3−1

Evaluate the logarithm. - log⁡8512\log _ { 8 } 512log8​512

Write an equivalent expression in exponential form. - log⁡216=4\log _ { 2 } 16 = 4log2​16=4

Solve the problem. -Let f(x) compute the cost of a rental car after x days of use at $40 per day. What does f-1(x) compute?

Decide whether the given functions are inverses. -

Solve the equation and express the solution in exact form. - log⁡4(x−5)+log⁡4(x−5)=1\log _ { 4 } ( x - 5 ) + \log _ { 4 } ( x - 5 ) = 1log4​(x−5)+log4​(x−5)=1

Provide an appropriate response. -The graph of an exponential function with base a is given. Sketch the graph of h(x) = a-x. Give the domain and range of h. f(x)=aXf(x)=a^{X}f(x)=aX

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - f(x)=(x+8)2f ( x ) = ( x + 8 ) ^ { 2 }f(x)=(x+8)2

For the function as defined that is one-to-one, graph f and f-1 on the same axes. - f(x)=5xf ( x ) = \frac { 5 } { x }f(x)=x5​

For the function as defined that is one-to-one, graph f and f-1 on the same axes. - f(x)=4xf ( x ) = 4 xf(x)=4x

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. - f(x)=2+xx,g(x)=2x−1f ( x ) = \frac { 2 + x } { x } , \quad g ( x ) = \frac { 2 } { x - 1 }f(x)=x2+x​,g(x)=x−12​

Graph the function. Give the domain and range. - f(x)=log⁡1/3(x+2)f(x)=\log _{1 / 3}(x+2)f(x)=log1/3​(x+2)

An everyday activity is described. Keeping in mind that an inverse operation ʺundoesʺ what an operation does, describe each inverse activity. -opening a door

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Solve the equation. Round to the nearest thousandth. - $168 ( 1.31 ) ^ { x / 2 } = 336$

Solve the equation. - $\left( \frac { 3 } { 7 } \right) ^ { x } = \frac { 2401 } { 81 }$

Write the word or phrase that best completes each statement or answers the question. -Without solving the inequality, what are the restrictions on $x$ if $\log _ { 2 } ( x - 3 ) - \log _ { 2 } ( x + 5 ) \leq$ 4? Explain.

The graph of a function f is given. Use the graph to find the indicated value. - $f ^ { - 1 } ( 3 )$ $The graph of a function f is given. Use the graph to find the indicated value. - f ^ { - 1 } ( 3 )$

Graph the function. - $f(x)=\left(\frac{3}{5}\right)^{x}$ $Graph the function. - f(x)=\left(\frac{3}{5}\right)^{x}$

Write the word or phrase that best completes each statement or answers the question. -How long will it take for prices in the economy to double at a $12 \%$ annual inflation rate?

Graph the exponential function using transformations where appropriate. - $f(x)=3^{x-3}-1$ $Graph the exponential function using transformations where appropriate. - f(x)=3^{x-3}-1$

Evaluate the logarithm. - $\log _ { 8 } 512$

Write an equivalent expression in exponential form. - $\log _ { 2 } 16 = 4$

Solve the equation and express the solution in exact form. - $\log _ { 4 } ( x - 5 ) + \log _ { 4 } ( x - 5 ) = 1$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = ( x + 8 ) ^ { 2 }$

For the function as defined that is one-to-one, graph f and f-1 on the same axes. - $f ( x ) = \frac { 5 } { x }$ $For the function as defined that is one-to-one, graph f and f-1 on the same axes. - f ( x ) = \frac { 5 } { x }$

For the function as defined that is one-to-one, graph f and f-1 on the same axes. - $f ( x ) = 4 x$

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = \frac { 2 + x } { x } , \quad g ( x ) = \frac { 2 } { x - 1 }$

Graph the function. Give the domain and range. - $f(x)=\log _{1 / 3}(x+2)$ $Graph the function. Give the domain and range. - f(x)=\log _{1 / 3}(x+2)$