Question 1

Find the function value. If the result is irrational, round your answer to the nearest thousandth.
-Let $f ( x ) = 2 ^ { x }$. Find $f ( 2.49 )$.

Accepted Answer

A)  $11.236$ 
B)  $4.98$ 
C)  $5.618$ 
D)  $8.427$ 
A)  $11.236$ 
B)  $4.98$ 
C)  $5.618$ 
D)  $8.427$

Question 2

Solve for the indicated variable.
-$\log _ { s } ( z + y ) = \log _ { s } ( 2 z - 4 ) , \quad$ for $y$

Accepted Answer

A)  $y = \frac { \log _ { \mathrm { s } } \mathrm { z } } { 4 }$ 
B)  $y = \log _ { S } ( z - 4 )$ 
C)  $\mathrm { y } = \mathrm { z } - 4$ 
D)  $y = \frac { z } { 4 }$ 
A)  $y = \frac { \log _ { \mathrm { s } } \mathrm { z } } { 4 }$ 
B)  $y = \log _ { S } ( z - 4 )$ 
C)  $\mathrm { y } = \mathrm { z } - 4$ 
D)  $y = \frac { z } { 4 }$

Question 3

Graph the function. Give the domain and range.
-$f(x)=\log _{5} x+4$

Accepted Answer

A)  domain: $( - \infty , 0 )$; range: $( - \infty , \infty )$
  
B)  domain: $( - \infty , \infty )$; range: $( 4 , \infty )$
  
C)  domain: $( 0 , \infty )$; range: $( - \infty , \infty )$
  
D)  domain: $( - 4 , \infty )$; range: $( - \infty , 0 )$
  
A)  domain: $( - \infty , 0 )$; range: $( - \infty , \infty )$
  
B)  domain: $( - \infty , \infty )$; range: $( 4 , \infty )$
  
C)  domain: $( 0 , \infty )$; range: $( - \infty , \infty )$
  
D)  domain: $( - 4 , \infty )$; range: $( - \infty , 0 )$

Question 4

Determine whether the statement is true or false.
-If a function f has an inverse, then the graph of f-1 can be obtained by reflecting the graph of f
across the x-axis.

Accepted Answer

A) True 
 B)False

Question 5

The graph of a function f is given. Use the graph to find the indicated value.
-$\mathrm { f } ^ { - 1 } ( 2 )$

Accepted Answer

A)  2 
B)  4 
C)  0 
D)  $1.4$ 
A)  2 
B)  4 
C)  0 
D)  $1.4$

Question 6

Use the change of base rule to find the logarithm to four decimal places.
-$\log \sqrt { 9 } 193.3$

Accepted Answer

A)  $0.4771$ 
B)  $4.7917$ 
C)  $0.2087$ 
D)  $2.3959$ 
A)  $0.4771$ 
B)  $4.7917$ 
C)  $0.2087$ 
D)  $2.3959$

Question 7

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$9 \mathrm { e } ^ { 2.2 \mathrm { x } } = 50$

Accepted Answer

A)  $\{ 0.78 \}$ 
B)  $\{ 1.71 \}$ 
C)  $\{ 5.14 \}$ 
D)  $\{ 3.77 \}$ 
A)  $\{ 0.78 \}$ 
B)  $\{ 1.71 \}$ 
C)  $\{ 5.14 \}$ 
D)  $\{ 3.77 \}$

Question 8

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to solve the problem.
-Encode the message BEWARE OF DOG using the one-to-one function defined by $$f ( x ) = x ^ { 3 } - 1$$ Give the inverse function that the decoder would need when the message is
received.

Accepted Answer

The answer of Use the alphabet coding method (A =1,...

Question 9

Solve the problem. Round your answer to the nearest tenth, when appropriate. Use the formula $$\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$$ as needed.
-Find the $\mathrm { pH }$ if $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] = 1.0 \times 10 ^ { - 2 }$.

Accepted Answer

A)  $- 12$ 
B)  2 
C)  $- 2$ 
D)  12 
A)  $- 12$ 
B)  2 
C)  $- 2$ 
D)  12

Question 10

Evaluate the logarithm.
-$\log _ { 10 } 100$

Accepted Answer

A)  200 
B)  -2 
C)  2 
D)  100 
A)  200 
B)  -2 
C)  2 
D)  100

Question 11

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log _ { 19 } \left( \frac { 11 \mathrm {~m} } { \mathrm {~s} } \right)$

Accepted Answer

A)  $\log _ { 19 } 11 - \log _ { 19 } m - \log _ { 19 } s$ 
B)  $\frac { \log _ { 19 } 11 + \log _ { 19 } \mathrm {~m} } { \log 19 \mathrm {~s} }$ 
C)  $\log _ { 19 } 11 + \log 19 m - \log _ { 19 } \mathrm {~s}$ 
D)  $\left( \log _ { 19 } 11 \right) ( \log 19 \mathrm {~m} ) - \log _ { 19 } \mathrm {~s}$ 
A)  $\log _ { 19 } 11 - \log _ { 19 } m - \log _ { 19 } s$ 
B)  $\frac { \log _ { 19 } 11 + \log _ { 19 } \mathrm {~m} } { \log 19 \mathrm {~s} }$ 
C)  $\log _ { 19 } 11 + \log 19 m - \log _ { 19 } \mathrm {~s}$ 
D)  $\left( \log _ { 19 } 11 \right) ( \log 19 \mathrm {~m} ) - \log _ { 19 } \mathrm {~s}$

Question 12

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

Accepted Answer

A)  $- 2 x + 2 - 5$ 
B)  $- 2 ^ { x - 2 } + 5$ 
C)  $- 2 x + 2 + 5$ 
D)  $2 ^ { x - 2 } - 5$ 
A)  $- 2 x + 2 - 5$ 
B)  $- 2 ^ { x - 2 } + 5$ 
C)  $- 2 x + 2 + 5$ 
D)  $2 ^ { x - 2 } - 5$

Question 13

Determine the function value.
-Suppose $f ( x ) = \log _ { a } x$ and $f ( 9 ) = 2$. Find $f \left( \frac { 1 } { 81 } \right)$.

Accepted Answer

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

Question 14

Decide whether the pair of functions graphed are inverses.
-

Accepted Answer

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

Question 15

Evaluate the logarithm.
-$\log _ { 2 } \sqrt { 2 }$

Accepted Answer

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

Question 16

Graph the function. Give the domain and range.
-

Accepted Answer

A)  domain: $( - 5 , \infty )$; range: $( 0 , \infty )$
  
B)  domain: $( - 5 , \infty )$; range: $( - \infty , \infty )$
  
C)  domain: $( 5 , \infty )$; range: $( 0 , \infty )$
  
D)  domain: $( - \infty , - 5 )$; range: $( 0 , \infty )$
  
A)  domain: $( - 5 , \infty )$; range: $( 0 , \infty )$
  
B)  domain: $( - 5 , \infty )$; range: $( - \infty , \infty )$
  
C)  domain: $( 5 , \infty )$; range: $( 0 , \infty )$
  
D)  domain: $( - \infty , - 5 )$; range: $( 0 , \infty )$

Question 17

Determine whether or not the function is one-to-one.
-$$f ( x ) = \frac { 8 } { x - 8 }$$

Accepted Answer

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

Question 18

Write in logarithmic form.
-$$3 ^ { 2 } = 9$$

Accepted Answer

A)  $\log _ { 9 } 3 = 2$ 
B)  $\log _ { 3 } 2 = 9$ 
C)  $\log _ { 3 } 9 = 2$ 
D)  $\log _ { 2 } 9 = 3$ 
A)  $\log _ { 9 } 3 = 2$ 
B)  $\log _ { 3 } 2 = 9$ 
C)  $\log _ { 3 } 9 = 2$ 
D)  $\log _ { 2 } 9 = 3$

Question 19

Write the word or phrase that best completes each statement or answers the question.
-Suppose $f ( x ) = 33.1 + 1.4 \log ( x + 1 )$ models salinity of ocean water to depths of 1000 meters at a certain latitude. $x$ is the depth in meters and $f ( x )$ is in grams of salt per kilogram of seawater. Approximate the salinity (to the nearest hundredth) when the depth is 262 meters.

Accepted Answer

A)  $78.70 \mathrm {~g} / \mathrm { kg }$ 
B)  $36.49 \mathrm {~g} / \mathrm { kg }$ 
C)  $- 29.71 \mathrm {~g} / \mathrm { kg }$ 
D)  $81.50 \mathrm {~g} / \mathrm { kg }$ 
A)  $78.70 \mathrm {~g} / \mathrm { kg }$ 
B)  $36.49 \mathrm {~g} / \mathrm { kg }$ 
C)  $- 29.71 \mathrm {~g} / \mathrm { kg }$ 
D)  $81.50 \mathrm {~g} / \mathrm { kg }$

Question 20

Solve the equation.
-$$2 ( 8 - 2 x ) = 4$$

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ 4 \}$ 
A)  $\{ 2 \}$ 
B)  $\{ - 3 \}$ 
C)  $\{ 3 \}$ 
D)  $\{ 4 \}$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = 2 ^ { x }$ . Find $f ( 2.49 )$ .

Solve for the indicated variable. - $\log _ { s } ( z + y ) = \log _ { s } ( 2 z - 4 ) , \quad$ for $y$

Graph the function. Give the domain and range. - $f(x)=\log _{5} x+4$ $Graph the function. Give the domain and range. - f(x)=\log _{5} x+4$

Determine whether the statement is true or false. -If a function f has an inverse, then the graph of f-1 can be obtained by reflecting the graph of f across the x-axis.

The graph of a function f is given. Use the graph to find the indicated value. - $\mathrm { f } ^ { - 1 } ( 2 )$ $The graph of a function f is given. Use the graph to find the indicated value. - \mathrm { f } ^ { - 1 } ( 2 )$

Use the change of base rule to find the logarithm to four decimal places. - $\log \sqrt { 9 } 193.3$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $9 \mathrm { e } ^ { 2.2 \mathrm { x } } = 50$

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to solve the problem. -Encode the message BEWARE OF DOG using the one-to-one function defined by $f ( x ) = x ^ { 3 } - 1$ Give the inverse function that the decoder would need when the message is received.

Evaluate the logarithm. - $\log _ { 10 } 100$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { 19 } \left( \frac { 11 \mathrm {~m} } { \mathrm {~s} } \right)$

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

Determine the function value. -Suppose $f ( x ) = \log _ { a } x$ and $f ( 9 ) = 2$ . Find $f \left( \frac { 1 } { 81 } \right)$ .

Decide whether the pair of functions graphed are inverses. -

Evaluate the logarithm. - $\log _ { 2 } \sqrt { 2 }$

Graph the function. Give the domain and range. -

Determine whether or not the function is one-to-one. - $f ( x ) = \frac { 8 } { x - 8 }$

Write in logarithmic form. - $3 ^ { 2 } = 9$

Solve the equation. - $2 ( 8 - 2 x ) = 4$

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

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let f(x)=2xf ( x ) = 2 ^ { x }f(x)=2x . Find f(2.49)f ( 2.49 )f(2.49) .

Solve for the indicated variable. - log⁡s(z+y)=log⁡s(2z−4),\log _ { s } ( z + y ) = \log _ { s } ( 2 z - 4 ) , \quadlogs​(z+y)=logs​(2z−4), for yyy

Graph the function. Give the domain and range. - f(x)=log⁡5x+4f(x)=\log _{5} x+4f(x)=log5​x+4