Question 1

Solve the equation.
-$\log x ^ { 2 } = 8$

Accepted Answer

A)  $\pm 2.828$ 
B)  $\pm 10,000$ 
C)  $673.977$ 
D)  $10 ^ { 8 }$ 
A)  $\pm 2.828$ 
B)  $\pm 10,000$ 
C)  $673.977$ 
D)  $10 ^ { 8 }$

Question 2

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry,
boundedness, extrema, asymptotes, and end behavior.
-$$f ( x ) = 4 \cdot 3 ^ { x }$$

Accepted Answer

@#IMG-DLM&
The domain is all real numbers, and the

Question 3

Evaluate the logarithm.
-$\log _ { 7 } \left( \frac { 1 } { 7 } \right)$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  0 
D)  7 
A)  1 
B)  $- 1$ 
C)  0 
D)  7

Question 4

Solve the equation by changing it to exponential form.
-$\log x = - 3$

Accepted Answer

A)  $x = - 30$ 
B)  $x = 30$ 
C)  $x = \frac { 1 } { 10 ^ { 3 } }$ 
D)  $x = \frac { 1 } { 3 ^ { 10 } }$ 
A)  $x = - 30$ 
B)  $x = 30$ 
C)  $x = \frac { 1 } { 10 ^ { 3 } }$ 
D)  $x = \frac { 1 } { 3 ^ { 10 } }$

Question 5

Solve the equation.
-$$\frac { 900 } { 1 + 99 \mathrm { e } ^ { - 0.3 \mathrm { t } } } = 225$$

Accepted Answer

A)  $13.174$ 
B)  $6.098$ 
C)  $11.655$ 
D)  $9.003$ 
A)  $13.174$ 
B)  $6.098$ 
C)  $11.655$ 
D)  $9.003$

Question 6

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of
logarithms or multiples of logarithms.
-$\log 4 x ^ { 4 }$

Accepted Answer

A)  $4 \log _ { 4 } x$ 
B)  $\log _ { 4 } 4 \mathrm { x }$ 
C)  $\log 44 \cdot \log _ { 4 } x$ 
D)  $\log _ { 4 } 4$ 
A)  $4 \log _ { 4 } x$ 
B)  $\log _ { 4 } 4 \mathrm { x }$ 
C)  $\log 44 \cdot \log _ { 4 } x$ 
D)  $\log _ { 4 } 4$

Question 7

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry,
boundedness, extrema, asymptotes, and end behavior.
-$$f ( x ) = 3 \cdot e ^ { 2 x }$$

Accepted Answer

@#IMG-DLM&
The domain is all real numbers, and the

Question 8

Use a calculator to find an approximate solution to the equation.
-$0.273 e ^ { 0.03 x } = 0.000273$

Accepted Answer

A)  $230.258509$ 
B)  $- 100$ 
C)  $- 230.25851$ 
D)  No solution 
A)  $230.258509$ 
B)  $- 100$ 
C)  $- 230.25851$ 
D)  No solution

Question 9

Determine the function which corresponds to the given graph.
- 
The asymptote is $x = 4$

Accepted Answer

A)  $y = \log ( x - 4 )$ 
B)  $y = - \log ( x - 4 )$ 
C)  $y = \log ( 4 - x )$ 
D)  $y = - \log ( x + 4 )$ 
A)  $y = \log ( x - 4 )$ 
B)  $y = - \log ( x - 4 )$ 
C)  $y = \log ( 4 - x )$ 
D)  $y = - \log ( x + 4 )$

Question 10

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end
behavior.
-f(x) = log1/2(x - 1)

Accepted Answer

@#IMG-DLM&
The domain is @#LAT-DLM&, and the range

Question 11

Solve the equation.
-log (x - 9) = 1 - log x

Accepted Answer

A)  -10, 1 
B)  -1, 10 
C)  -10 
D)  10 
A)  -10, 1 
B)  -1, 10 
C)  -10 
D)  10

Question 12

Determine a formula for the exponential function.
-The graph of an exponential function is given. Which of the following is the correct equation of the function?

Accepted Answer

A)  $y = 0.45 ^ { \mathrm { x } }$ 
B)  $y = 0.31 ^ { x }$ 
C)  $\mathrm { y } = 1.8 ^ { \mathrm { x } }$ 
D)  $y = 2.4 ^ { \mathrm { x } }$ 
A)  $y = 0.45 ^ { \mathrm { x } }$ 
B)  $y = 0.31 ^ { x }$ 
C)  $\mathrm { y } = 1.8 ^ { \mathrm { x } }$ 
D)  $y = 2.4 ^ { \mathrm { x } }$

Question 13

Provide an appropriate response.
-$$\text { Explain how the graph of } y = ( 1 / 4 ) ^ { x } + 1 \text { can be obtained from the graph of } y = 4 ^ { x } \text {. }$$

Accepted Answer

The graph is reflect

Question 14

Solve the problem.
-In September 1998 the population of the country of West Goma in millions was modeled by $\mathrm { f } ( \mathrm { x } ) = 16.4 \mathrm { e } ^ { 0.0002 \mathrm { x } }$. At the same time the population of East Goma in millions was modeled by $g ( x ) = 13.7 e ^ { 0.0134 x }$. In both formulas $\mathrm { x }$ is the year, where $\mathrm { x } = 0$ corresponds to September 1998. Assuming these trends continue, estimate the year when the population of West Goma will equal the population of East Goma.

Accepted Answer

A)  14 
B)  1984 
C)  2011 
D)  2012 
A)  14 
B)  1984 
C)  2011 
D)  2012

Question 15

Find the amount accumulated after investing a principal P for t years at an interest rate r.
-P = $800, t = 4, r = 1% compounded continuously

Accepted Answer

A)  $832.65 
B)  $1027.22 
C)  $43,678.52 
D)  $1116.49 
A)  $832.65 
B)  $1027.22 
C)  $43,678.52 
D)  $1116.49

Question 16

Find the domain of the function.
-$$f ( x ) = \ln ( 4 - x )$$

Accepted Answer

A)  $( - \infty , - 4 )$ 
B)  $( 4 , \infty )$ 
C)  $( - x , 4 )$ 
D)  $( - 4 , \infty )$ 
A)  $( - \infty , - 4 )$ 
B)  $( 4 , \infty )$ 
C)  $( - x , 4 )$ 
D)  $( - 4 , \infty )$

Question 17

Solve the inequality graphically.
-$$5 ^ { x } > 2 ^ { x }$$

Accepted Answer

A)  $x  1$ 
C)  $x  0$ 
A)  $x  1$ 
C)  $x  0$

Question 18

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of
logarithms or multiples of logarithms.
-$\log \sqrt [ 3 ] { \frac { x } { y } }$

Accepted Answer

A)  $\frac { \log x } { \log y }$ 
B)  $\frac { 1 } { 3 } \log x - \frac { 1 } { 3 } \log y$ 
C)  $\log \left( \frac { x } { 3 } \right) - \log \left( \frac { y } { 3 } \right)$ 
D)  $\frac { \log ( \sqrt [ 3 ] { x } ) } { \log ( \sqrt [ 3 ] { y } ) }$ 
A)  $\frac { \log x } { \log y }$ 
B)  $\frac { 1 } { 3 } \log x - \frac { 1 } { 3 } \log y$ 
C)  $\log \left( \frac { x } { 3 } \right) - \log \left( \frac { y } { 3 } \right)$ 
D)  $\frac { \log ( \sqrt [ 3 ] { x } ) } { \log ( \sqrt [ 3 ] { y } ) }$

Question 19

Decide if the function is an exponential function. If it is, state the initial value and the base.
-$$\mathrm { y } = 3.8 ^ { \mathrm { x } }$$

Accepted Answer

A)  Not an exponential function 
B)  Exponential Function; base $= 3.8$; initial value $= 0$ 
C)  Exponential Function; base $= 3.8$; initial value $= 1$ 
D)  Exponential Function; base $= x$; initial value $= 3.8$ 
A)  Not an exponential function 
B)  Exponential Function; base $= 3.8$; initial value $= 0$ 
C)  Exponential Function; base $= 3.8$; initial value $= 1$ 
D)  Exponential Function; base $= x$; initial value $= 3.8$

Question 20

Use the change of base rule to find the logarithm to four decimal places.
-$\log _ { 6.6 } 210$

Accepted Answer

A)  $0.3529$ 
B)  $31.8182$ 
C)  $2.8336$ 
D)  $2.3222$ 
A)  $0.3529$ 
B)  $31.8182$ 
C)  $2.8336$ 
D)  $2.3222$

Solve the equation. - $\log x ^ { 2 } = 8$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = 4 \cdot 3 ^ { x }$

Evaluate the logarithm. - $\log _ { 7 } \left( \frac { 1 } { 7 } \right)$

Solve the equation by changing it to exponential form. - $\log x = - 3$

Solve the equation. - $\frac { 900 } { 1 + 99 \mathrm { e } ^ { - 0.3 \mathrm { t } } } = 225$

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. - $\log 4 x ^ { 4 }$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = 3 \cdot e ^ { 2 x }$

Use a calculator to find an approximate solution to the equation. - $0.273 e ^ { 0.03 x } = 0.000273$

Determine the function which corresponds to the given graph. - The asymptote is $x = 4$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. -f(x) = log1/2(x - 1)

Solve the equation. -log (x - 9) = 1 - log x

Determine a formula for the exponential function. -The graph of an exponential function is given. Which of the following is the correct equation of the function?

Provide an appropriate response. - $\text { Explain how the graph of } y = ( 1 / 4 ) ^ { x } + 1 \text { can be obtained from the graph of } y = 4 ^ { x } \text {. }$

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $800, t = 4, r = 1% compounded continuously

Find the domain of the function. - $f ( x ) = \ln ( 4 - x )$

Solve the inequality graphically. - $5 ^ { x } > 2 ^ { x }$

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. - $\log \sqrt [ 3 ] { \frac { x } { y } }$

Decide if the function is an exponential function. If it is, state the initial value and the base. - $\mathrm { y } = 3.8 ^ { \mathrm { x } }$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 6.6 } 210$

Functions and Graphs

Polynomial, Power, and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 3: Exponential, Logistic, and Logarithmic Functions

Solve the equation. - log⁡x2=8\log x ^ { 2 } = 8logx2=8

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - f(x)=4⋅3xf ( x ) = 4 \cdot 3 ^ { x }f(x)=4⋅3x

Evaluate the logarithm. - log⁡7(17)\log _ { 7 } \left( \frac { 1 } { 7 } \right)log7​(71​)

Solve the equation by changing it to exponential form. - log⁡x=−3\log x = - 3logx=−3

Solve the equation. - 9001+99e−0.3t=225\frac { 900 } { 1 + 99 \mathrm { e } ^ { - 0.3 \mathrm { t } } } = 2251+99e−0.3t900​=225

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. - log⁡4x4\log 4 x ^ { 4 }log4x4

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - f(x)=3⋅e2xf ( x ) = 3 \cdot e ^ { 2 x }f(x)=3⋅e2x

Use a calculator to find an approximate solution to the equation. - 0.273e0.03x=0.0002730.273 e ^ { 0.03 x } = 0.0002730.273e0.03x=0.000273

Determine the function which corresponds to the given graph. - The asymptote is x=4x = 4x=4