Question 1

Determine the function value.
-Suppose $f ( x ) = \log _ { a } ( x )$ and $f ( 11 ) = 2$. Find $f \left( \frac { \sqrt { 11 } } { 11 } \right)$

Accepted Answer

A)  -1 
B)  1 
C)  2 
D)  $- 2$ 
A)  -1 
B)  1 
C)  2 
D)  $- 2$

Question 2

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

Accepted Answer

A)  domain: $( \infty , 2 )$; range: $( \infty , \infty )$
  
B)  domain: $( - 2 , \infty )$; range: $( \infty , \infty )$
  
C)  domain: $( - 2 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( \infty , 2 )$; range: $( \infty , \infty )$
  
A)  domain: $( \infty , 2 )$; range: $( \infty , \infty )$
  
B)  domain: $( - 2 , \infty )$; range: $( \infty , \infty )$
  
C)  domain: $( - 2 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( \infty , 2 )$; range: $( \infty , \infty )$

Question 3

Provide an appropriate response.
-Explain how the graph of $$y = \left( \frac { 1 } { 4 } \right) ^ { x } + 2 \text { can be obtained from the graph of } y = 4 ^ { x }$$

Accepted Answer

The graph is reflect

Question 4

A certain country's Consumer Price Index is approximated by A( $\mathrm { A } ( \mathrm { t } ) = 100 \mathrm { e } ^ { 0.024 \mathrm { t } }$ , where t represents the number of years. Use the function to determine the year in which costs will be 50% higher than in year 0.

Accepted Answer

A)  year 13 
B)  year 15 
C)  year 19 
D)  year 17 
A)  year 13 
B)  year 15 
C)  year 19 
D)  year 17

Question 5

Given $f ( x ) = \ln x$, evaluate the following.
(a) $\mathrm { f } \left( \mathrm { e } ^ { 4 } \right)$
(b) $f \left( e ^ { \ln 4 } \right)$
(c) $f \left( e ^ { 2 } \ln 4 \right)$

Accepted Answer

(a) 4 (b)

Question 6

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

Accepted Answer

A)  domain: $( \infty , \infty )$; range: $( 0 , \infty )$
  
B)  domain: $( \infty , \infty )$; range: $( \infty , 0 )$
  
C)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
A)  domain: $( \infty , \infty )$; range: $( 0 , \infty )$
  
B)  domain: $( \infty , \infty )$; range: $( \infty , 0 )$
  
C)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( 0 , \infty )$; range: $( \infty , \infty )$

Question 7

Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$. Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the function $\ln$. $\ln \left( \sqrt [ 3 ] { a b ^ { 4 } } \right)$

Accepted Answer

A)  $\frac { \mathrm { u } } { 3 } - \frac { 4 } { 3 } \mathrm { v }$ 
B)  $\frac { u } { 3 } + \frac { 4 } { 3 } v$ 
C)  $\frac { 4 } { 3 } u + \frac { 4 } { 3 } v$ 
D)  $\frac { \mathrm { u } } { 3 } - 4 \mathrm { v }$ 
A)  $\frac { \mathrm { u } } { 3 } - \frac { 4 } { 3 } \mathrm { v }$ 
B)  $\frac { u } { 3 } + \frac { 4 } { 3 } v$ 
C)  $\frac { 4 } { 3 } u + \frac { 4 } { 3 } v$ 
D)  $\frac { \mathrm { u } } { 3 } - 4 \mathrm { v }$

Question 8

Use the graph of f to sketch a graph of the inverse of f using a dashed curve.
-

Accepted Answer

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

Question 9

Solve the equation.
-$\left( \frac { 16 } { 9 } \right) ^ { x + 1 } = \left( \frac { 3 } { 4 } \right) ^ { x - 1 }$

Accepted Answer

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

Question 10

Match the function with its graph.
-$$f ( x ) = \log _ { 2 } \left( \frac { x } { 2 } \right)$$

Accepted Answer

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

Question 11

Solve the equation and express the solution in exact form.
-$\ln \mathrm { e } ^ { \mathrm { x } } - \ln \mathrm { e } ^ { 7 } = \ln \mathrm { e } ^ { 4 }$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ 11 \}$ 
D)  $\{ 28 \}$ 
A)  $\{ 3 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ 11 \}$ 
D)  $\{ 28 \}$

Question 12

Graph the exponential function using transformations where appropriate.
-

Accepted Answer

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

Question 13

If $f ( x ) = \log _ { 5 } x$, find $f \left( 5 ^ { 5 \log 5^{5} } \right)$.

Accepted Answer

A)  0 
B)  5 
C)  1 
D)  25 
A)  0 
B)  5 
C)  1 
D)  25

Question 14

Use the definition of inverses to determine whether f and g are inverses.
-$f ( x ) = 5 x + 25 , \quad g ( x ) = \frac { 1 } { 5 } x - 5$

Accepted Answer

A) True 
 B)False

Question 15

Match the function with its graph.
-$$f ( x ) = \log _ { 3 } ( - x )$$

Accepted Answer

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

Question 16

Solve for the indicated variable.
-$v = p - k \ln t$, for $t$

Accepted Answer

A)  $t = \ln \frac { p - v } { k }$ 
B)  $t = e ( p - v ) / k$ 
C)  $\mathrm { t } = \frac { \mathrm { p } - \mathrm { v } } { \mathrm { k } }$ 
D)  $t = e ^ { ( v - p ) / k }$ 
A)  $t = \ln \frac { p - v } { k }$ 
B)  $t = e ( p - v ) / k$ 
C)  $\mathrm { t } = \frac { \mathrm { p } - \mathrm { v } } { \mathrm { k } }$ 
D)  $t = e ^ { ( v - p ) / k }$

Question 17

Determine whether or not the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Question 18

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $\log _ { 2 } ( x - 8 ) - 1$ 
B)  $\log _ { 2 } ( - x + 8 ) - 1$ 
C)  $\log _ { 2 } ( x - 8 ) + 1$ 
D)  $\log _ { 2 } ( - x + 8 ) + 1$ 
A)  $\log _ { 2 } ( x - 8 ) - 1$ 
B)  $\log _ { 2 } ( - x + 8 ) - 1$ 
C)  $\log _ { 2 } ( x - 8 ) + 1$ 
D)  $\log _ { 2 } ( - x + 8 ) + 1$

Question 19

For the function as defined that is one-to-one, graph f and $\mathrm { f } ^ { - 1 }$ on the same axes.
-$f(x)=\sqrt{x+4}$

Accepted Answer

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

Question 20

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or
reflected.
-

Accepted Answer

A)  $\log _ { 2 } ( x + 1 ) + 1$ 
B)  $\log _ { 2 } ( x - 1 ) + 1$ 
C)  $\log _ { 2 } ( x + 1 ) - 1$ 
D)  $\log _ { 2 } ( x - 1 ) - 1$ 
A)  $\log _ { 2 } ( x + 1 ) + 1$ 
B)  $\log _ { 2 } ( x - 1 ) + 1$ 
C)  $\log _ { 2 } ( x + 1 ) - 1$ 
D)  $\log _ { 2 } ( x - 1 ) - 1$

Determine the function value. -Suppose $f ( x ) = \log _ { a } ( x )$ and $f ( 11 ) = 2$ . Find $f \left( \frac { \sqrt { 11 } } { 11 } \right)$

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

Provide an appropriate response. -Explain how the graph of $y = \left( \frac { 1 } { 4 } \right) ^ { x } + 2 \text { can be obtained from the graph of } y = 4 ^ { x }$

A certain country's Consumer Price Index is approximated by A( $\mathrm { A } ( \mathrm { t } ) = 100 \mathrm { e } ^ { 0.024 \mathrm { t } }$ , where t represents the number of years. Use the function to determine the year in which costs will be 50% higher than in year 0.

Given $f ( x ) = \ln x$ , evaluate the following. (a) $\mathrm { f } \left( \mathrm { e } ^ { 4 } \right)$ (b) $f \left( e ^ { \ln 4 } \right)$ (c) $f \left( e ^ { 2 } \ln 4 \right)$

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

Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$ . Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the function $\ln$ . $\ln \left( \sqrt [ 3 ] { a b ^ { 4 } } \right)$

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Solve the equation. - $\left( \frac { 16 } { 9 } \right) ^ { x + 1 } = \left( \frac { 3 } { 4 } \right) ^ { x - 1 }$

Match the function with its graph. - $f ( x ) = \log _ { 2 } \left( \frac { x } { 2 } \right)$

Solve the equation and express the solution in exact form. - $\ln \mathrm { e } ^ { \mathrm { x } } - \ln \mathrm { e } ^ { 7 } = \ln \mathrm { e } ^ { 4 }$

Graph the exponential function using transformations where appropriate. -

If $f ( x ) = \log _ { 5 } x$ , find $f \left( 5 ^ { 5 \log 5^{5} } \right)$ .

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = 5 x + 25 , \quad g ( x ) = \frac { 1 } { 5 } x - 5$

Match the function with its graph. - $f ( x ) = \log _ { 3 } ( - x )$

Solve for the indicated variable. - $v = p - k \ln t$ , for $t$

Determine whether or not the function is one-to-one. -

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

For the function as defined that is one-to-one, graph f and $\mathrm { f } ^ { - 1 }$ on the same axes. - $f(x)=\sqrt{x+4}$ $For the function as defined that is one-to-one, graph f and \mathrm { f } ^ { - 1 } on the same axes. - f(x)=\sqrt{x+4}$

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Determine the function value. -Suppose f(x)=log⁡a(x)f ( x ) = \log _ { a } ( x )f(x)=loga​(x) and f(11)=2f ( 11 ) = 2f(11)=2 . Find f(1111)f \left( \frac { \sqrt { 11 } } { 11 } \right)f(1111​​)

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

Provide an appropriate response. -Explain how the graph of y=(14)x+2 can be obtained from the graph of y=4xy = \left( \frac { 1 } { 4 } \right) ^ { x } + 2 \text { can be obtained from the graph of } y = 4 ^ { x }y=(41​)x+2 can be obtained from the graph of y=4x

Given f(x)=ln⁡xf ( x ) = \ln xf(x)=lnx , evaluate the following. (a) f(e4)\mathrm { f } \left( \mathrm { e } ^ { 4 } \right)f(e4) (b) f(eln⁡4)f \left( e ^ { \ln 4 } \right)f(eln4) (c) f(e2ln⁡4)f \left( e ^ { 2 } \ln 4 \right)f(e2ln4)

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

Let u=ln⁡a\mathrm { u } = \ln \mathrm { a }u=lna and v=ln⁡b\mathrm { v } = \ln \mathrm { b }v=lnb . Write the following expression in terms of u\mathrm { u }u and v\mathrm { v }v without using the function ln⁡\lnln . ln⁡(ab43)\ln \left( \sqrt [ 3 ] { a b ^ { 4 } } \right)ln(3ab4​)

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Solve the equation. - (169)x+1=(34)x−1\left( \frac { 16 } { 9 } \right) ^ { x + 1 } = \left( \frac { 3 } { 4 } \right) ^ { x - 1 }(916​)x+1=(43​)x−1

Match the function with its graph. - f(x)=log⁡2(x2)f ( x ) = \log _ { 2 } \left( \frac { x } { 2 } \right)f(x)=log2​(2x​)

Solve the equation and express the solution in exact form. - ln⁡ex−ln⁡e7=ln⁡e4\ln \mathrm { e } ^ { \mathrm { x } } - \ln \mathrm { e } ^ { 7 } = \ln \mathrm { e } ^ { 4 }lnex−lne7=lne4

Graph the exponential function using transformations where appropriate. -

If f(x)=log⁡5xf ( x ) = \log _ { 5 } xf(x)=log5​x , find f(55log⁡55)f \left( 5 ^ { 5 \log 5^{5} } \right)f(55log55) .

Use the definition of inverses to determine whether f and g are inverses. - f(x)=5x+25,g(x)=15x−5f ( x ) = 5 x + 25 , \quad g ( x ) = \frac { 1 } { 5 } x - 5f(x)=5x+25,g(x)=51​x−5

Match the function with its graph. - f(x)=log⁡3(−x)f ( x ) = \log _ { 3 } ( - x )f(x)=log3​(−x)

Solve for the indicated variable. - v=p−kln⁡tv = p - k \ln tv=p−klnt , for ttt

Determine whether or not the function is one-to-one. -

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

For the function as defined that is one-to-one, graph f and f−1\mathrm { f } ^ { - 1 }f−1 on the same axes. - f(x)=x+4f(x)=\sqrt{x+4}f(x)=x+4​

Write an equation for the graph given. The graph represents an logarithmic function f with base 2 or 3, translated and/or reflected. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Determine the function value. -Suppose $f ( x ) = \log _ { a } ( x )$ and $f ( 11 ) = 2$ . Find $f \left( \frac { \sqrt { 11 } } { 11 } \right)$

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

Provide an appropriate response. -Explain how the graph of $y = \left( \frac { 1 } { 4 } \right) ^ { x } + 2 \text { can be obtained from the graph of } y = 4 ^ { x }$

Given $f ( x ) = \ln x$ , evaluate the following. (a) $\mathrm { f } \left( \mathrm { e } ^ { 4 } \right)$ (b) $f \left( e ^ { \ln 4 } \right)$ (c) $f \left( e ^ { 2 } \ln 4 \right)$

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

Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$ . Write the following expression in terms of $\mathrm { u }$ and $\mathrm { v }$ without using the function $\ln$ . $\ln \left( \sqrt [ 3 ] { a b ^ { 4 } } \right)$

Solve the equation. - $\left( \frac { 16 } { 9 } \right) ^ { x + 1 } = \left( \frac { 3 } { 4 } \right) ^ { x - 1 }$

Match the function with its graph. - $f ( x ) = \log _ { 2 } \left( \frac { x } { 2 } \right)$

Solve the equation and express the solution in exact form. - $\ln \mathrm { e } ^ { \mathrm { x } } - \ln \mathrm { e } ^ { 7 } = \ln \mathrm { e } ^ { 4 }$

If $f ( x ) = \log _ { 5 } x$ , find $f \left( 5 ^ { 5 \log 5^{5} } \right)$ .

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = 5 x + 25 , \quad g ( x ) = \frac { 1 } { 5 } x - 5$

Match the function with its graph. - $f ( x ) = \log _ { 3 } ( - x )$

Solve for the indicated variable. - $v = p - k \ln t$ , for $t$

For the function as defined that is one-to-one, graph f and $\mathrm { f } ^ { - 1 }$ on the same axes. - $f(x)=\sqrt{x+4}$ $For the function as defined that is one-to-one, graph f and \mathrm { f } ^ { - 1 } on the same axes. - f(x)=\sqrt{x+4}$