Question 1

Write the word or phrase that best completes each statement or answers the question.
-

Accepted Answer

A)  $353 \mathrm { mg }$ 
B)  $343 \mathrm { mg }$ 
C)  $177 \mathrm { mg }$ 
D)  $420 \mathrm { mg }$ 
A)  $353 \mathrm { mg }$ 
B)  $343 \mathrm { mg }$ 
C)  $177 \mathrm { mg }$ 
D)  $420 \mathrm { mg }$

Question 2

Find the domain and range of the inverse of the given function.
-$$f ( x ) = \frac { 2 } { x + 1 }$$

Accepted Answer

A)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: all real numbers; range: $( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
D)  Domain and range: all real numbers 
A)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: all real numbers; range: $( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
D)  Domain and range: all real numbers

Question 3

Given $$\log _ { 10 } 2 = 0.3010 \text { and } \log _ { 10 } 3 = 0.4771 \text {, }$$ find the logarithm without using a calculator.
-$$\log _ { 10 } \sqrt { 24 }$$

Accepted Answer

A)  0.6901 
B)  1.0792 
C)  0.5396 
D)  1.1748 
A)  0.6901 
B)  1.0792 
C)  0.5396 
D)  1.1748

Question 4

Find the present value of the future value.
-$3000, invested for 3 years at 5% compounded monthly

Accepted Answer

A)  $3484.42 
B)  $2582.93 
C)  $3469.42 
D)  $2597.93 
A)  $3484.42 
B)  $2582.93 
C)  $3469.42 
D)  $2597.93

Question 5

Write the word or phrase that best completes each statement or answers the question.
-$$\text { Explain how to solve } e ^ { 2 x } + 4 e ^ { x } - 21 = 0 \text { analytically. }$$

Accepted Answer

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

Question 6

Solve the equation.
-$\log _ { x } 4 = - 2$

Accepted Answer

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

Question 7

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-2x = 10

Accepted Answer

A)  {5.00} 
B)  {0.30} 
C)  {1.61} 
D)  {3.32} 
A)  {5.00} 
B)  {0.30} 
C)  {1.61} 
D)  {3.32}

Question 8

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers.
-$$\left( \log _ { a } x - \log _ { a } y \right) + 6 \log _ { a } z$$

Accepted Answer

A)  $\log _ { a } \left( \frac { x z ^ { 6 } } { y } \right)$ 
B)  $\log _ { a } \left( \frac { 6 x z } { y } \right)$ 
C)  $\log _ { a } \left( \frac { x } { z ^ { 6 } y } \right)$ 
D)  $\log _ { a } \left( x + z ^ { 6 } - y \right)$ 
A)  $\log _ { a } \left( \frac { x z ^ { 6 } } { y } \right)$ 
B)  $\log _ { a } \left( \frac { 6 x z } { y } \right)$ 
C)  $\log _ { a } \left( \frac { x } { z ^ { 6 } y } \right)$ 
D)  $\log _ { a } \left( x + z ^ { 6 } - y \right)$

Question 9

Solve the equation.
-$$\log _ { ( x + 2 ) } 11 = 1$$

Accepted Answer

A)  $\{ - 9 \}$ 
B)  $\{ 11 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 13 \}$ 
A)  $\{ - 9 \}$ 
B)  $\{ 11 \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 13 \}$

Question 10

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log _ { 2 } ( 9 x + 9 y )$

Accepted Answer

A)  $\log _ { 2 } 81 x y$ 
B)  $\left( \log _ { 2 } 9 x \right) \left( \log _ { 2 } 9 y \right)$ 
C)  $\log _ { 2 } ( 9 x + 9 y )$ 
D)  $\log _ { 2 } 9 x + \log _ { 2 } 9 y$ 
A)  $\log _ { 2 } 81 x y$ 
B)  $\left( \log _ { 2 } 9 x \right) \left( \log _ { 2 } 9 y \right)$ 
C)  $\log _ { 2 } ( 9 x + 9 y )$ 
D)  $\log _ { 2 } 9 x + \log _ { 2 } 9 y$

Question 11

Find the value. Give an approximation to four decimal places.
-$\log 226 + \log 20$

Accepted Answer

A)  $16.2385$ 
B)  $8.4163$ 
C)  $3.0628$ 
D)  $3.6551$ 
A)  $16.2385$ 
B)  $8.4163$ 
C)  $3.0628$ 
D)  $3.6551$

Question 12

Write the word or phrase that best completes each statement or answers the question.
-In the formula $\mathrm { N } = \mathrm { Ie } k t , \mathrm {~N}$ is the number of items in terms of an initial population I at a given time $\mathrm { t }$ and $\mathrm { k }$ is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain country to triple if its annual growth rate is $7.3 \%$ ? Round to the nearest year.

Accepted Answer

A)  $15 \mathrm { yr }$ 
B)  $7 \mathrm { yr }$ 
C)  $1 \mathrm { yr }$ 
D)  $41 \mathrm { yr }$ 
A)  $15 \mathrm { yr }$ 
B)  $7 \mathrm { yr }$ 
C)  $1 \mathrm { yr }$ 
D)  $41 \mathrm { yr }$

Question 13

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

Accepted Answer

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

Question 14

Solve the problem.
-Let f(x) compute the time in hours to travel x miles at 60 miles per hour. What is the interpretation of f -1(9)?

Accepted Answer

A)  The miles traveled in 9 hours at 60 miles per hour 
B)  The hours taken to travel 9 miles at 60 miles per hour 
C)  The hours taken to travel 60 miles 
D)  The miles traveled in 60 hours 
A)  The miles traveled in 9 hours at 60 miles per hour 
B)  The hours taken to travel 9 miles at 60 miles per hour 
C)  The hours taken to travel 60 miles 
D)  The miles traveled in 60 hours

Question 15

Solve the equation.
-$$a ^ { 3 / 4 } = 27$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\{ - 3,3 \}$ 
C)  $\{ 81 \}$ 
D)  $\{ - 81,81 \}$ 
A)  $\{ 3 \}$ 
B)  $\{ - 3,3 \}$ 
C)  $\{ 81 \}$ 
D)  $\{ - 81,81 \}$

Question 16

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function.
-$$f ( x ) = \frac { x + 1 } { x - 4 } ; [ - 10,10 ] \text { by } [ - 10,10 ]$$

Accepted Answer

A)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 \mathrm { x } - 1 } { \mathrm { x } + 1 }$ 
B)  not one-to-one 
C)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 4 } { \mathrm { x } + 1 }$ 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 1 } { \mathrm { x } - 1 }$ 
A)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 \mathrm { x } - 1 } { \mathrm { x } + 1 }$ 
B)  not one-to-one 
C)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 4 } { \mathrm { x } + 1 }$ 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 1 } { \mathrm { x } - 1 }$

Question 17

Find the value. Give an approximation to four decimal places.
-$\log 3534$

Accepted Answer

A)  $3.5495$ 
B)  $3.5483$ 
C)  $8.1702$ 
D)  $3.5470$ 
A)  $3.5495$ 
B)  $3.5483$ 
C)  $8.1702$ 
D)  $3.5470$

Question 18

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers.
-$3 \log _ { m } y - 7 \log _ { m } x ^ { 2 }$

Accepted Answer

A)  $\log _ { m } \left( \frac { 3 y } { 7 x ^ { 2 } } \right)$ 
B)  $\log _ { m } \left( \frac { \mathrm { y } ^ { 3 } } { \mathrm { x } ^ { 14 } } \right)$ 
C)  $\log _ { m } \left( \frac { y ^ { 3 } } { x ^ { 9 } } \right)$ 
D)  $\frac { \log _ { m } \mathrm { y } ^ { 3 } } { \log _ { \mathrm { m } } 14 }$ 
A)  $\log _ { m } \left( \frac { 3 y } { 7 x ^ { 2 } } \right)$ 
B)  $\log _ { m } \left( \frac { \mathrm { y } ^ { 3 } } { \mathrm { x } ^ { 14 } } \right)$ 
C)  $\log _ { m } \left( \frac { y ^ { 3 } } { x ^ { 9 } } \right)$ 
D)  $\frac { \log _ { m } \mathrm { y } ^ { 3 } } { \log _ { \mathrm { m } } 14 }$

Question 19

Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\mathrm { e } ^ { \mathrm { x } } + \ln \mathrm { x } = 7$$

Accepted Answer

A)  $\{ 3.621 \}$ 
B)  $\{ 1.854 \}$ 
C)  $\{ 2.854 \}$ 
D)  $\{ 1.259 \}$ 
A)  $\{ 3.621 \}$ 
B)  $\{ 1.854 \}$ 
C)  $\{ 2.854 \}$ 
D)  $\{ 1.259 \}$

Question 20

Solve the problem.
-Find the required annual interest rate, to the nearest tenth of a percent, for $5100 to grow to $6400 if interest is compounded quarterly for 7 years.

Accepted Answer

A)  0.8% 
B)  3.3% 
C)  4.1% 
D)  1.6% 
A)  0.8% 
B)  3.3% 
C)  4.1% 
D)  1.6%

Write the word or phrase that best completes each statement or answers the question. -

Find the domain and range of the inverse of the given function. - $f ( x ) = \frac { 2 } { x + 1 }$

Given $\log _ { 10 } 2 = 0.3010 \text { and } \log _ { 10 } 3 = 0.4771 \text {, }$ find the logarithm without using a calculator. - $\log _ { 10 } \sqrt { 24 }$

Find the present value of the future value. -$3000, invested for 3 years at 5% compounded monthly

Write the word or phrase that best completes each statement or answers the question. - $\text { Explain how to solve } e ^ { 2 x } + 4 e ^ { x } - 21 = 0 \text { analytically. }$

Solve the equation. - $\log _ { x } 4 = - 2$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. -2x = 10

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers. - $\left( \log _ { a } x - \log _ { a } y \right) + 6 \log _ { a } z$

Solve the equation. - $\log _ { ( x + 2 ) } 11 = 1$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { 2 } ( 9 x + 9 y )$

Find the value. Give an approximation to four decimal places. - $\log 226 + \log 20$

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

Solve the problem. -Let f(x) compute the time in hours to travel x miles at 60 miles per hour. What is the interpretation of f -1(9)?

Solve the equation. - $a ^ { 3 / 4 } = 27$

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = \frac { x + 1 } { x - 4 } ; [ - 10,10 ] \text { by } [ - 10,10 ]$

Find the value. Give an approximation to four decimal places. - $\log 3534$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers. - $3 \log _ { m } y - 7 \log _ { m } x ^ { 2 }$

Solve the following graphically. If necessary, round answers to the nearest thousandth. - $\mathrm { e } ^ { \mathrm { x } } + \ln \mathrm { x } = 7$

Solve the problem. -Find the required annual interest rate, to the nearest tenth of a percent, for $5100 to grow to $6400 if interest is compounded quarterly for 7 years.

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

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Exam 4: Inverse, Exponential, and Logarithmic Functions