Question 1

Determine whether or not the function is one-to-one.
-$f(x)=3 x^{2}-5$

Accepted Answer

A) True 
 B)False

Question 2

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.
-$f(x)=\sqrt{x+2}$

Accepted Answer

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

Question 3

The screen shows a table of values for the function defined by $Y_{1}=\left(0.95+\frac{1}{X}\right)^{X}$.
 
Why is there an error message for $\mathrm{x}=0$ ?

Accepted Answer

A)  The calculator made a mistake. 
B)  The value of the function is too large for the calculator to comprehend. 
C)  An exponent of zero is not defined. 
D)  Division by zero is not defined. 
A)  The calculator made a mistake. 
B)  The value of the function is too large for the calculator to comprehend. 
C)  An exponent of zero is not defined. 
D)  Division by zero is not defined.

Question 4

Find the amount of money in an account after 3 years if $\$ 3300$ is deposited at $6 \%$ annual interest compounded semiannually.

Accepted Answer

A)  $\$ 3949.05$ 
B)  $\$ 3945.54$ 
C)  $\$ 3930.35$ 
D)  $\$ 3940.37$ 
A)  $\$ 3949.05$ 
B)  $\$ 3945.54$ 
C)  $\$ 3930.35$ 
D)  $\$ 3940.37$

Question 5

Why is e used as a base for exponential and logarithmic functions?

Accepted Answer

Answers may vary. One possibility: e is

Question 6

Use a calculator and the change-of-base formula to find the logarithm to four decimal places.
-$\log _{6} 43.73$

Accepted Answer

A)  7.2883 
B)  0.4743 
C)  1.6408 
D)  2.1086 
A)  7.2883 
B)  0.4743 
C)  1.6408 
D)  2.1086

Question 7

Write in exponential form.
-$\log _{1 / 64} \frac{1}{2}=\frac{1}{6}$

Accepted Answer

A)  $\left(\frac{1}{2}\right)^{1 / 6}=\frac{1}{64}$ 
B)  $\left(\frac{1}{64}\right)^{1 / 2}=\frac{1}{6}$ 
C)  $\left(\frac{1}{6}\right)^{1 / 64}=\frac{1}{2}$ 
D)  $\left(\frac{1}{64}\right)^{1 / 6}=\frac{1}{2}$ 
A)  $\left(\frac{1}{2}\right)^{1 / 6}=\frac{1}{64}$ 
B)  $\left(\frac{1}{64}\right)^{1 / 2}=\frac{1}{6}$ 
C)  $\left(\frac{1}{6}\right)^{1 / 64}=\frac{1}{2}$ 
D)  $\left(\frac{1}{64}\right)^{1 / 6}=\frac{1}{2}$

Question 8

Why is finding the value of $\log _{a} a^{6}$ like answering the question "What is the name of the girl whose name is Jane?"

Accepted Answer

Answers may vary. One possibility: Like

Question 9

Determine whether or not the function is one-to-one.
-$\{(6,6),(7,6),(8,4),(9,-6)\}$

Accepted Answer

A) True 
 B)False

Question 10

When solving a logarithmic equation, why must you always check that each solution works in the original equation?

Accepted Answer

Some solutions may r

Question 11

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated.
-$\mathrm{e}^{0.461 \mathrm{x}}=28$

Accepted Answer

A)  $\{3.332\}$ 
B)  $\{7.228\}$ 
C)  $\{1.536\}$ 
D)  $\{0.138\}$ 
A)  $\{3.332\}$ 
B)  $\{7.228\}$ 
C)  $\{1.536\}$ 
D)  $\{0.138\}$

Question 12

Using the exponential key of a calculator to find an approximation to the nearest thousandth.
-2.5973 .8

Accepted Answer

A)  9.869 
B)  32.04 
C)  6.744 
D)  37.583 
A)  9.869 
B)  32.04 
C)  6.744 
D)  37.583

Question 13

Write in exponential form.
-$\log \pi\left(\pi^{7}\right)=x$

Accepted Answer

A)  $\{7\}$ 
B)  $\left\{7^{3}\right\}$ 
C)  $\{3\}$ 
D)  $\{37\}$ 
A)  $\{7\}$ 
B)  $\left\{7^{3}\right\}$ 
C)  $\{3\}$ 
D)  $\{37\}$

Question 14

Find the logarithm. Give an approximation to four decimal places
-$\ln 0.000333$

Accepted Answer

A)  -8.0074 
B)  8.0074 
C)  3.4776 
D)  -3.4776 
A)  -8.0074 
B)  8.0074 
C)  3.4776 
D)  -3.4776

Question 15

Evaluate the logarithm.
-$\log _{1 / 9} 9$

Accepted Answer

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

Question 16

Write in logarithmic form.
-$7^{2}=49$

Accepted Answer

A)  $\log _{7} 2=49$ 
B)  $\log _{49} 7=2$ 
C)  $\log _{7} 49=2$ 
D)  $\log _{2} 49=7$ 
A)  $\log _{7} 2=49$ 
B)  $\log _{49} 7=2$ 
C)  $\log _{7} 49=2$ 
D)  $\log _{2} 49=7$

Question 17

Solve, giving the correct solution to four decimal places.
-$22 x=29$

Accepted Answer

A)  $\{1.2763\}$ 
B)  $\{1.3182\}$ 
C)  $\{1.0894\}$ 
D)  $\{0.9200\}$ 
A)  $\{1.2763\}$ 
B)  $\{1.3182\}$ 
C)  $\{1.0894\}$ 
D)  $\{0.9200\}$

Question 18

Is it possible to solve the equation $7 \mathrm{X}=4$ by taking the natural logarithm of 4 , the common logarithm of 7 , and finding the quotient $\frac{\ln 4}{\log 7}$ ? Explain.

Accepted Answer

No. You must either take the n

Question 19

Use a calculator and the change-of-base formula to find the logarithm to four decimal places.
-$\log _{28} 77.11$

Accepted Answer

A)  1.3040 
B)  1.8871 
C)  2.7539 
D)  0.7669 
A)  1.3040 
B)  1.8871 
C)  2.7539 
D)  0.7669

Question 20

Explain how exponential and logarithmic functions are related.

Accepted Answer

Answers may vary. One possibility: Expon

Determine whether or not the function is one-to-one. - $f(x)=3 x^{2}-5$

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $f(x)=\sqrt{x+2}$ $Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - f(x)=\sqrt{x+2}$

Find the amount of money in an account after 3 years if $\$ 3300$ is deposited at $6 \%$ annual interest compounded semiannually.

Why is e used as a base for exponential and logarithmic functions?

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. - $\log _{6} 43.73$

Write in exponential form. - $\log _{1 / 64} \frac{1}{2}=\frac{1}{6}$

Why is finding the value of $\log _{a} a^{6}$ like answering the question "What is the name of the girl whose name is Jane?"

Determine whether or not the function is one-to-one. - $\{(6,6),(7,6),(8,4),(9,-6)\}$

When solving a logarithmic equation, why must you always check that each solution works in the original equation?

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{0.461 \mathrm{x}}=28$

Using the exponential key of a calculator to find an approximation to the nearest thousandth. -2.5973 .8

Write in exponential form. - $\log \pi\left(\pi^{7}\right)=x$

Find the logarithm. Give an approximation to four decimal places - $\ln 0.000333$

Evaluate the logarithm. - $\log _{1 / 9} 9$

Write in logarithmic form. - $7^{2}=49$

Solve, giving the correct solution to four decimal places. - $22 x=29$

Is it possible to solve the equation $7 \mathrm{X}=4$ by taking the natural logarithm of 4 , the common logarithm of 7 , and finding the quotient $\frac{\ln 4}{\log 7}$ ? Explain.

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. - $\log _{28} 77.11$

Explain how exponential and logarithmic functions are related.

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 10: Inverse, Exponential, and Logarithmic Functions

Determine whether or not the function is one-to-one. - f(x)=3x2−5f(x)=3 x^{2}-5f(x)=3x2−5

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - f(x)=x+2f(x)=\sqrt{x+2}f(x)=x+2​

The screen shows a table of values for the function defined by Y1=(0.95+1X)XY_{1}=\left(0.95+\frac{1}{X}\right)^{X}Y1​=(0.95+X1​)X . Why is there an error message for x=0\mathrm{x}=0x=0 ?

Find the amount of money in an account after 3 years if $3300\$ 3300$3300 is deposited at 6%6 \%6% annual interest compounded semiannually.

Why is e used as a base for exponential and logarithmic functions?

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. - log⁡643.73\log _{6} 43.73log6​43.73

Write in exponential form. - log⁡1/6412=16\log _{1 / 64} \frac{1}{2}=\frac{1}{6}log1/64​21​=61​

Why is finding the value of log⁡aa6\log _{a} a^{6}loga​a6 like answering the question "What is the name of the girl whose name is Jane?"

Determine whether or not the function is one-to-one. - {(6,6),(7,6),(8,4),(9,−6)}\{(6,6),(7,6),(8,4),(9,-6)\}{(6,6),(7,6),(8,4),(9,−6)}

When solving a logarithmic equation, why must you always check that each solution works in the original equation?

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - e0.461x=28\mathrm{e}^{0.461 \mathrm{x}}=28e0.461x=28

Using the exponential key of a calculator to find an approximation to the nearest thousandth. -2.5973 .8

Write in exponential form. - log⁡π(π7)=x\log \pi\left(\pi^{7}\right)=xlogπ(π7)=x

Find the logarithm. Give an approximation to four decimal places - ln⁡0.000333\ln 0.000333ln0.000333

Evaluate the logarithm. - log⁡1/99\log _{1 / 9} 9log1/9​9

Write in logarithmic form. - 72=497^{2}=4972=49

Solve, giving the correct solution to four decimal places. - 22x=2922 x=2922x=29

Is it possible to solve the equation 7X=47 \mathrm{X}=47X=4 by taking the natural logarithm of 4 , the common logarithm of 7 , and finding the quotient ln⁡4log⁡7\frac{\ln 4}{\log 7}log7ln4​ ? Explain.

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. - log⁡2877.11\log _{28} 77.11log28​77.11

Explain how exponential and logarithmic functions are related.

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Determine whether or not the function is one-to-one. - $f(x)=3 x^{2}-5$

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $f(x)=\sqrt{x+2}$ $Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - f(x)=\sqrt{x+2}$

Find the amount of money in an account after 3 years if $\$ 3300$ is deposited at $6 \%$ annual interest compounded semiannually.

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. - $\log _{6} 43.73$

Write in exponential form. - $\log _{1 / 64} \frac{1}{2}=\frac{1}{6}$

Why is finding the value of $\log _{a} a^{6}$ like answering the question "What is the name of the girl whose name is Jane?"

Determine whether or not the function is one-to-one. - $\{(6,6),(7,6),(8,4),(9,-6)\}$

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise indicated. - $\mathrm{e}^{0.461 \mathrm{x}}=28$

Write in exponential form. - $\log \pi\left(\pi^{7}\right)=x$

Find the logarithm. Give an approximation to four decimal places - $\ln 0.000333$

Evaluate the logarithm. - $\log _{1 / 9} 9$

Write in logarithmic form. - $7^{2}=49$

Solve, giving the correct solution to four decimal places. - $22 x=29$

Is it possible to solve the equation $7 \mathrm{X}=4$ by taking the natural logarithm of 4 , the common logarithm of 7 , and finding the quotient $\frac{\ln 4}{\log 7}$ ? Explain.

Use a calculator and the change-of-base formula to find the logarithm to four decimal places. - $\log _{28} 77.11$