Question 1

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$2 ( x - 1 ) = 18$$

Accepted Answer

A)  $\{ 4.32 \}$ 
B)  $\{ 5.17 \}$ 
C)  $\{ 3.17 \}$ 
D)  $\{ 10.00 \}$ 
A)  $\{ 4.32 \}$ 
B)  $\{ 5.17 \}$ 
C)  $\{ 3.17 \}$ 
D)  $\{ 10.00 \}$

Question 2

Determine whether the statement is true or false.
-If $\mathrm { f }$ is a one-to-one function and the graph of $\mathrm { f }$ lies completely within the first quadrant, then the graph of $\mathrm { f } ^ { - 1 }$ lies completely within the first quadrant.

Accepted Answer

A) True 
 B)False

Question 3

Given $$\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$$ find the logarithm without using a calculator.
-$\log _ { 10 } 6$

Accepted Answer

A)  $0.9542$ 
B)  $0.1436$ 
C)  $0.903$ 
D)  $0.7781$ 
A)  $0.9542$ 
B)  $0.1436$ 
C)  $0.903$ 
D)  $0.7781$

Question 4

Choose the one alternative that best completes the 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 $\mathrm { S } _ { 0 } = 1.00 \times 10 ^ { - 12 } \mathrm { watt } / \mathrm { m } ^ { 2 }$. What is the intensity in watt $/ \mathrm { m } ^ { 2 }$ of a noise measured at 82 decibels? (Round to the nearest tenth.)

Accepted Answer

A)  $8.2 \times 10 ^ { - 10 }$ watt $/ \mathrm { m } ^ { 2 }$ 
B)  $1.6 \times 10 ^ { - 4 }$ watt $/ \mathrm { m } ^ { 2 }$ 
C)  $1.6 \times 10 ^ { - 3 }$ watt $/ \mathrm { m } ^ { 2 }$ 
D)  $3.6 \times 10 ^ { 15 }$ watt $/ \mathrm { m } ^ { 2 }$ 
A)  $8.2 \times 10 ^ { - 10 }$ watt $/ \mathrm { m } ^ { 2 }$ 
B)  $1.6 \times 10 ^ { - 4 }$ watt $/ \mathrm { m } ^ { 2 }$ 
C)  $1.6 \times 10 ^ { - 3 }$ watt $/ \mathrm { m } ^ { 2 }$ 
D)  $3.6 \times 10 ^ { 15 }$ watt $/ \mathrm { m } ^ { 2 }$

Question 5

Choose the one alternative that best completes the statement or answers the question.
-Suppose $f ( x ) = 34.2 + 1.2 \log ( x + 1 )$ 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 752 meters.

Accepted Answer

A)  $97.19 \mathrm {~g} / \mathrm { kg }$ 
B)  $99.59 \mathrm {~g} / \mathrm { kg }$ 
C)  $- 30.75 \mathrm {~g} / \mathrm { kg }$ 
D)  $37.65 \mathrm {~g} / \mathrm { kg }$ 
A)  $97.19 \mathrm {~g} / \mathrm { kg }$ 
B)  $99.59 \mathrm {~g} / \mathrm { kg }$ 
C)  $- 30.75 \mathrm {~g} / \mathrm { kg }$ 
D)  $37.65 \mathrm {~g} / \mathrm { kg }$

Question 6

Solve the equation. Give the answer in exact form.
-$$5 ^ { 2 x } - 3 \left( 5 ^ { x } \right) = 40$$

Accepted Answer

A)  $\left\{ \log _ { 5 } 8 , \log _ { 5 } ( - 5 ) \right\}$ 
B)  $\left\{ \log _ { 5 } 8 \right\}$ 
C)  $\{ 5 \ln 8,5 \ln ( - 5 ) \}$ 
D)  $\{ 5 \ln 8 \}$ 
A)  $\left\{ \log _ { 5 } 8 , \log _ { 5 } ( - 5 ) \right\}$ 
B)  $\left\{ \log _ { 5 } 8 \right\}$ 
C)  $\{ 5 \ln 8,5 \ln ( - 5 ) \}$ 
D)  $\{ 5 \ln 8 \}$

Question 7

Write an equivalent expression in exponential form.
-$$\log \sqrt { 7 } 343 = 6$$

Accepted Answer

A)  $343 ^ { 3 } = 7$ 
B)  $7^{343} = 3$ 
C)  $3 ^ { 7 } = 343$ 
D)  $7 ^ { 3 } = 343$ 
A)  $343 ^ { 3 } = 7$ 
B)  $7^{343} = 3$ 
C)  $3 ^ { 7 } = 343$ 
D)  $7 ^ { 3 } = 343$

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Solve the problem.
-What is the rate on an investment that triples $3272 in 27 years? Assume interest is compounded monthly.

Accepted Answer

A)  5.1% 
B)  2.7% 
C)  3.4% 
D)  4.1% 
A)  5.1% 
B)  2.7% 
C)  3.4% 
D)  4.1%

Question 12

Find the future value.
-$4603 invested for 2 years at 3% compounded annually

Accepted Answer

A)  $4885.46 
B)  $4887.27 
C)  $4886.54 
D)  $4883.32 
A)  $4885.46 
B)  $4887.27 
C)  $4886.54 
D)  $4883.32

Question 13

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-$$f ( x ) = 7 x ^ { 3 } - 6$$

Accepted Answer

A)  not a one-to-one 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 6 } { 7 } }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 6 } { 7 } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } } { 7 } } + 6$ 
A)  not a one-to-one 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 6 } { 7 } }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 6 } { 7 } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } } { 7 } } + 6$

Question 14

Choose the one alternative that best completes the statement or answers the question.
-A population is increasing according to the exponential function defined by y $$y = 3 e ^ { - 04 x }$$ , where y is in millions and x is the number of years. Which of the following should be done in order to answer
The question "How long will it take for the population to quadruple?"

Accepted Answer

A)  Solve $3 e ^ { \cdot 04 x } = 4$ 
B)  Solve $3 e ^ {\cdot 04 x} = 12$. 
C)  Evaluate $y = 3 \mathrm { e } ^ { .04 ( 1 / 4 ) }$ 
D)  Evaluate y $= 3 \mathrm { e } ^ { .04 ( 4 ) }$. 
A)  Solve $3 e ^ { \cdot 04 x } = 4$ 
B)  Solve $3 e ^ {\cdot 04 x} = 12$. 
C)  Evaluate $y = 3 \mathrm { e } ^ { .04 ( 1 / 4 ) }$ 
D)  Evaluate y $= 3 \mathrm { e } ^ { .04 ( 4 ) }$.

Question 15

Find the value. Give an approximation to four decimal places.
-The logarithmic function $f ( x ) = - 100 + 87 \ln x$ models the number of visitors (in millions) to a certain country's museums, where $x$ is the number of years since the initial recording of the number of visitors. Use this function to estimate the number of visitors in year 60 . Round to the nearest tenth of a year.

Accepted Answer

A)  $384.3$ million 
B)  $256.2$ million 
C)  $192.2$ million 
D)  $128.1$ million 
A)  $384.3$ million 
B)  $256.2$ million 
C)  $192.2$ million 
D)  $128.1$ million

Question 16

Use the definition of inverses to determine whether f and g are inverses.
-$f ( x ) = \sqrt { x + 5 } , x \geq - 5 ; g ( x ) = x ^ { 2 } + 5$

Accepted Answer

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

Question 17

Solve the equation. Give the answer in exact form.
-$$3 \mathrm { e } ^ { 2 \mathrm { x } } + 7 \mathrm { e } ^ { \mathrm { x } } = 20$$

Accepted Answer

A)  $\left\{ \ln \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ \ln \frac { 5 } { 3 } \right\}$ 
C)  $\left\{ \mathrm { e } ^ { 5 / 3 } , \mathrm { e } ^ { - 4 } \right\}$ 
D)  $\left\{ \ln \frac { 5 } { 3 } , \ln ( - 4 ) \right\}$ 
A)  $\left\{ \ln \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ \ln \frac { 5 } { 3 } \right\}$ 
C)  $\left\{ \mathrm { e } ^ { 5 / 3 } , \mathrm { e } ^ { - 4 } \right\}$ 
D)  $\left\{ \ln \frac { 5 } { 3 } , \ln ( - 4 ) \right\}$

Question 18

Solve the equation.
-$$m ^ { - 4 } = \frac { 1 } { 256 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 4 } \right\}$ 
B)  $\{ - 4,4 \}$ 
C)  $\{ 256 \}$ 
D)  $\{ 4 \}$ 
A)  $\left\{ \frac { 1 } { 4 } \right\}$ 
B)  $\{ - 4,4 \}$ 
C)  $\{ 256 \}$ 
D)  $\{ 4 \}$

Question 19

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 20

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

Accepted Answer

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

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 ( x - 1 ) = 18$

Determine whether the statement is true or false. -If $\mathrm { f }$ is a one-to-one function and the graph of $\mathrm { f }$ lies completely within the first quadrant, then the graph of $\mathrm { f } ^ { - 1 }$ lies completely within the first quadrant.

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator. - $\log _ { 10 } 6$

Solve the equation. Give the answer in exact form. - $5 ^ { 2 x } - 3 \left( 5 ^ { x } \right) = 40$

Write an equivalent expression in exponential form. - $\log \sqrt { 7 } 343 = 6$

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

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

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

Solve the problem. -What is the rate on an investment that triples $3272 in 27 years? Assume interest is compounded monthly.

Find the future value. -$4603 invested for 2 years at 3% compounded annually

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = 7 x ^ { 3 } - 6$

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = \sqrt { x + 5 } , x \geq - 5 ; g ( x ) = x ^ { 2 } + 5$

Solve the equation. Give the answer in exact form. - $3 \mathrm { e } ^ { 2 \mathrm { x } } + 7 \mathrm { e } ^ { \mathrm { x } } = 20$

Solve the equation. - $m ^ { - 4 } = \frac { 1 } { 256 }$

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

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

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

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 2(x−1)=182 ( x - 1 ) = 182(x−1)=18

Determine whether the statement is true or false. -If f\mathrm { f }f is a one-to-one function and the graph of f\mathrm { f }f lies completely within the first quadrant, then the graph of f−1\mathrm { f } ^ { - 1 }f−1 lies completely within the first quadrant.

Given log⁡102≈0.3010 and log⁡103≈0.4771\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771log10​2≈0.3010 and log10​3≈0.4771 find the logarithm without using a calculator. - log⁡106\log _ { 10 } 6log10​6

Solve the equation. Give the answer in exact form. - 52x−3(5x)=405 ^ { 2 x } - 3 \left( 5 ^ { x } \right) = 4052x−3(5x)=40

Write an equivalent expression in exponential form. - log⁡7343=6\log \sqrt { 7 } 343 = 6log7​343=6

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

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

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

Solve the problem. -What is the rate on an investment that triples $3272 in 27 years? Assume interest is compounded monthly.

Find the future value. -$4603 invested for 2 years at 3% compounded annually

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - f(x)=7x3−6f ( x ) = 7 x ^ { 3 } - 6f(x)=7x3−6

Use the definition of inverses to determine whether f and g are inverses. - f(x)=x+5,x≥−5;g(x)=x2+5f ( x ) = \sqrt { x + 5 } , x \geq - 5 ; g ( x ) = x ^ { 2 } + 5f(x)=x+5​,x≥−5;g(x)=x2+5

Solve the equation. Give the answer in exact form. - 3e2x+7ex=203 \mathrm { e } ^ { 2 \mathrm { x } } + 7 \mathrm { e } ^ { \mathrm { x } } = 203e2x+7ex=20

Solve the equation. - m−4=1256m ^ { - 4 } = \frac { 1 } { 256 }m−4=2561​

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

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

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

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 ( x - 1 ) = 18$

Determine whether the statement is true or false. -If $\mathrm { f }$ is a one-to-one function and the graph of $\mathrm { f }$ lies completely within the first quadrant, then the graph of $\mathrm { f } ^ { - 1 }$ lies completely within the first quadrant.

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator. - $\log _ { 10 } 6$

Solve the equation. Give the answer in exact form. - $5 ^ { 2 x } - 3 \left( 5 ^ { x } \right) = 40$

Write an equivalent expression in exponential form. - $\log \sqrt { 7 } 343 = 6$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = 7 x ^ { 3 } - 6$

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = \sqrt { x + 5 } , x \geq - 5 ; g ( x ) = x ^ { 2 } + 5$

Solve the equation. Give the answer in exact form. - $3 \mathrm { e } ^ { 2 \mathrm { x } } + 7 \mathrm { e } ^ { \mathrm { x } } = 20$

Solve the equation. - $m ^ { - 4 } = \frac { 1 } { 256 }$