Question 1

Determine whether or not the function is one-to-one.
-$f ( x ) = \frac { 4 x - 4 } { 9 x + 3 }$

Accepted Answer

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

Question 2

Find the present value of the future value.
-The decay of 291 mg of an isotope is given by A(t)= 291e-0.022t, where t is time in years since the initial amount of 291 mg was present. Find the amount (to the nearest milligram) left after 38 years.

Accepted Answer

A)  126 
B)  63 
C)  285 
D)  123 
A)  126 
B)  63 
C)  285 
D)  123

Question 3

Find the future value.
-$3742 invested for 12 years at 5% compounded quarterly 157)

Accepted Answer

A)  $6720.09 
B)  $6768.25 
C)  $6809.87 
D)  $6793.06 
A)  $6720.09 
B)  $6768.25 
C)  $6809.87 
D)  $6793.06

Question 4

For the function as defined that is one-to-one, graph f and $$\mathbf { f } ^ { - 1 }$$ on the same axes.
-$$f ( x ) = \frac { 2 } { x }$$

Accepted Answer

A) 
  
B)  Function is its own inverse
  
C) 
  
D)  Function is its own inverse
  
A) 
  
B)  Function is its own inverse
  
C) 
  
D)  Function is its own inverse

Question 5

Use the change of base rule to find the logarithm to four decimal places.
-$$\log _ { 2.3 } 262$$

Accepted Answer

A)  113.9130 
B)  6.6854 
C)  0.1496 
D)  2.4183 
A)  113.9130 
B)  6.6854 
C)  0.1496 
D)  2.4183

Question 6

Determine whether or not the function is one-to-one.
-$$f ( x ) = x ^ { 2 } + 5$$

Accepted Answer

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

Question 7

Write the word or phrase that best completes each statement or answers the question.
-$$\text { Without using a calculator, explain why } 2 \pi \text { must be greater than } 8 \text { but less than } 16 \text {. }$$

Accepted Answer

Since @#LAT-DLM&; that is @#LAT-DLM& is greater th

Question 8

Solve for the indicated variable.
-$A = \frac { W B } { 1 - ( 1 + z ) ^ { - s ^ { \prime } } }$, for $\mathrm { s }$

Accepted Answer

A)  $s = \frac { \ln A - \ln ( A - W B ) } { \ln ( 1 + z ) }$ 
B)  $s = \ln \frac { W } { ( A - A B ) ( 1 + z ) }$ 
C)  $s = \frac { \ln W } { \ln [ ( A - A B ) ( 1 - z ) ] }$ 
D)  $s = \ln \frac { A } { ( A - W B ) ( 1 + z ) }$ 
A)  $s = \frac { \ln A - \ln ( A - W B ) } { \ln ( 1 + z ) }$ 
B)  $s = \ln \frac { W } { ( A - A B ) ( 1 + z ) }$ 
C)  $s = \frac { \ln W } { \ln [ ( A - A B ) ( 1 - z ) ] }$ 
D)  $s = \ln \frac { A } { ( A - W B ) ( 1 + z ) }$

Question 9

Given $$\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$$ find the logarithm without using a calculator.
-$\log _ { 10 } \left( 18 ^ { 1 / 3 } \right)$

Accepted Answer

A)  $0.5187$ 
B)  $0.4184$ 
C)  $0.7782$ 
D)  $1.0787$ 
A)  $0.5187$ 
B)  $0.4184$ 
C)  $0.7782$ 
D)  $1.0787$

Question 10

Find the value. Give an approximation to four decimal places.
-$\log 0.00563$

Accepted Answer

A)  $- 2.2495$ 
B)  $- 2.2418$ 
C)  $- 5.1796$ 
D)  $- 2.2573$ 
A)  $- 2.2495$ 
B)  $- 2.2418$ 
C)  $- 5.1796$ 
D)  $- 2.2573$

Question 11

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-{(6, -7), (11, -6), (9, -5), (7, -4)}

Accepted Answer

A)  {(7, 6), (6, 11), (-5, 9), (-4, 7)} 
B)  {(6, -7), (11, -6), (9, -5), (7, -4)} 
C)  {(-7, 6), (-6, 11), (-5, 9), (-4, 7)} 
D)  not one-to-one 
A)  {(7, 6), (6, 11), (-5, 9), (-4, 7)} 
B)  {(6, -7), (11, -6), (9, -5), (7, -4)} 
C)  {(-7, 6), (-6, 11), (-5, 9), (-4, 7)} 
D)  not one-to-one

Question 12

Write in logarithmic form.
-$$6 ^ { 2 } = 36$$

Accepted Answer

A)  $\log _ { 36 } 6 = 2$ 
B)  $\log _ { 6 } 36 = 2$ 
C)  $\log _ { 2 } 36 = 6$ 
D)  $\log _ { 6 } 2 = 36$ 
A)  $\log _ { 36 } 6 = 2$ 
B)  $\log _ { 6 } 36 = 2$ 
C)  $\log _ { 2 } 36 = 6$ 
D)  $\log _ { 6 } 2 = 36$

Question 13

The graph of a function f is given. Use the graph to find the indicated value.
-Let f(x) compute the time in hours to travel x miles at 39 miles per hour. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Accepted Answer

A)  The hours taken to travel 39 miles 
B)  The miles traveled in x hours at 39 miles per hour 
C)  The hours taken to travel x miles at 39 miles per hour 
D)  The miles traveled in 39 hours 
A)  The hours taken to travel 39 miles 
B)  The miles traveled in x hours at 39 miles per hour 
C)  The hours taken to travel x miles at 39 miles per hour 
D)  The miles traveled in 39 hours

Question 14

Decide whether the given functions are inverses.
-$$\begin{array}{l}
\begin{array} { r | r } 
\mathrm { x } & \mathrm { f } ( \mathrm { x } ) \
\hline 1 & 1 \
- 2 & - 4 \
12 & - 5 \
10 & 5 \
0 & 7
\end{array}\
\begin{array} { r | c } 
x & g ( x ) \
\hline 1 & 1 \
4 & - 2 \
- 5 & 12 \
5 & 10 \
7 & 0
\end{array}
\end{array}$$

Accepted Answer

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

Question 15

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-{(13, -6), (-5, 5), (6, -20)}

Accepted Answer

A)  not one-to-one 
B)  {(13, 5), (13, -5), (-20, 6)} 
C)  {(-6, 13), (5, -5), (-20, 6)} 
D)  {(-6, 13), (6, -5), (-20, 5)} 
A)  not one-to-one 
B)  {(13, 5), (13, -5), (-20, 6)} 
C)  {(-6, 13), (5, -5), (-20, 6)} 
D)  {(-6, 13), (6, -5), (-20, 5)}

Question 16

Provide an appropriate response.
-What are the domain and range for the equation $y = 2 ^ { x }$ ?

Accepted Answer

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

Question 17

Provide an appropriate response.
-Explain how the graph of $$y = \left( \frac { 1 } { 4 } \right) ^ { x } - 5$$ can be obtained from the graph o $$y = 4 ^ { x }$$

Accepted Answer

The graph is reflect

Question 18

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\ln ( x + 2 ) = - \sqrt [ 3 ] { x + 5 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ - 1.8148 \}$ 
C)  $\{ - 1.7955 \}$ 
D)  $\{ - 1.772 \}$ 
A)  $\varnothing$ 
B)  $\{ - 1.8148 \}$ 
C)  $\{ - 1.7955 \}$ 
D)  $\{ - 1.772 \}$

Question 19

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

Accepted Answer

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

Question 20

Find the domain and range of the inverse of the given function.
-$$f ( x ) = \sqrt { x - 7 }$$

Accepted Answer

A)  Domain and range: all real numbers 
B)  Domain: $[ 0 , \infty )$; range: $[ 7 , \infty )$ 
C)  Domain: all real numbers; range: $[ 7 , \infty )$ 
D)  Domain: $[ 7 , \infty )$; range: $[ 0 , \infty )$ 
A)  Domain and range: all real numbers 
B)  Domain: $[ 0 , \infty )$; range: $[ 7 , \infty )$ 
C)  Domain: all real numbers; range: $[ 7 , \infty )$ 
D)  Domain: $[ 7 , \infty )$; range: $[ 0 , \infty )$

Determine whether or not the function is one-to-one. - $f ( x ) = \frac { 4 x - 4 } { 9 x + 3 }$

Find the present value of the future value. -The decay of 291 mg of an isotope is given by A(t)= 291e-0.022t, where t is time in years since the initial amount of 291 mg was present. Find the amount (to the nearest milligram) left after 38 years.

Find the future value. -$3742 invested for 12 years at 5% compounded quarterly 157)

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f ( x ) = \frac { 2 } { x }$ $For the function as defined that is one-to-one, graph f and \mathbf { f } ^ { - 1 } on the same axes. - f ( x ) = \frac { 2 } { x }$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 2.3 } 262$

Determine whether or not the function is one-to-one. - $f ( x ) = x ^ { 2 } + 5$

Write the word or phrase that best completes each statement or answers the question. - $\text { Without using a calculator, explain why } 2 \pi \text { must be greater than } 8 \text { but less than } 16 \text {. }$

Solve for the indicated variable. - $A = \frac { W B } { 1 - ( 1 + z ) ^ { - s ^ { \prime } } }$ , for $\mathrm { s }$

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator. - $\log _ { 10 } \left( 18 ^ { 1 / 3 } \right)$

Find the value. Give an approximation to four decimal places. - $\log 0.00563$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." -{(6, -7), (11, -6), (9, -5), (7, -4)}

Write in logarithmic form. - $6 ^ { 2 } = 36$

The graph of a function f is given. Use the graph to find the indicated value. -Let f(x) compute the time in hours to travel x miles at 39 miles per hour. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Decide whether the given functions are inverses. - () 1 1 -2 -4 12 -5 10 5 0 7 x g(x) 1 1 4 -2 -5 12 5 10 7 0

If the function is one-to-one, find its inverse. If not, write "not one-to-one." -{(13, -6), (-5, 5), (6, -20)}

Provide an appropriate response. -What are the domain and range for the equation $y = 2 ^ { x }$ ?

Provide an appropriate response. -Explain how the graph of $y = \left( \frac { 1 } { 4 } \right) ^ { x } - 5$ can be obtained from the graph o $y = 4 ^ { x }$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\ln ( x + 2 ) = - \sqrt [ 3 ] { x + 5 }$

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

Find the domain and range of the inverse of the given function. - $f ( x ) = \sqrt { x - 7 }$

Review of Basic Concepts

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

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Determine whether or not the function is one-to-one. - f(x)=4x−49x+3f ( x ) = \frac { 4 x - 4 } { 9 x + 3 }f(x)=9x+34x−4​