Question 1

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

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

Question 2

Choose the one alternative that best completes the statement or answers the question.
The graph of a logarithmic function is shown. Select the function which matches the graph.
-

Accepted Answer

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

Question 3

Choose the one alternative that best completes the statement or answers the question.
-A mechanic is testing the cooling system of a boat engine. He measures the engine's temperature over time. Use a graphing utility to fit a logistic function to the data. What is the carrying capacity of the cooling system?
$\begin{array}{l|lllll}
\text { time, min } & 5 & 10 & 15 & 20 & 25 \
\hline \text { temperature, }{ }^{\circ} \mathrm{F} & 100 & 180 & 270 & 300 & 305
\end{array}$

Accepted Answer

A)  $y = \frac { 306.53 } { 1 + 7.92 e ^ { - 0.254 x } } , 307 ^ { \circ } \mathrm { F }$ 
B)  $\mathrm { y } = \frac { 311.63 } { 1 + 8.1 \mathrm { e } ^ { - 0.253 \mathrm { x } } } , 312 ^ { \circ } \mathrm { F }$ 
C) $ \mathrm { y } = \frac { 314.79 } { 1 + 7.86 \mathrm { e } ^ { - 1.22 \mathrm { x } } } , 315 ^ { \circ } \mathrm { F }$ 
D)  $\mathrm { y } = \frac { 314.79 } { 1 + 7.86 \mathrm { e } ^ { - 0.246 \mathrm { x } } } , 315 ^ { \circ } \mathrm { F }$ 
A)  $y = \frac { 306.53 } { 1 + 7.92 e ^ { - 0.254 x } } , 307 ^ { \circ } \mathrm { F }$ 
B)  $\mathrm { y } = \frac { 311.63 } { 1 + 8.1 \mathrm { e } ^ { - 0.253 \mathrm { x } } } , 312 ^ { \circ } \mathrm { F }$ 
C) $ \mathrm { y } = \frac { 314.79 } { 1 + 7.86 \mathrm { e } ^ { - 1.22 \mathrm { x } } } , 315 ^ { \circ } \mathrm { F }$ 
D)  $\mathrm { y } = \frac { 314.79 } { 1 + 7.86 \mathrm { e } ^ { - 0.246 \mathrm { x } } } , 315 ^ { \circ } \mathrm { F }$

Question 4

Write the word or phrase that best completes each statement or answers the question.
-A rumor is spread at an elementary school with 1200 students according to the model $\mathrm { N } = 1200 \left( 1 - \mathrm { e } ^ { - 0.16 \mathrm {~d} } \right)$ where $\mathrm { N }$ is the number of students who have heard the rumor and $\mathrm { d }$ is the number of days that have elapsed since the rumor began. How many students will have heard the rumor after 5 days?

Accepted Answer

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

Question 5

Change the logarithmic expression to an equivalent expression involving an exponent.
-$\log _ { 5 } x = 2$

Accepted Answer

A)  $x ^ { 2 } = 5$ 
B)  $5 ^ { x } = 2$ 
C)  $5 ^ { 2 } = x$ 
D)  $2 ^ { 5 } = x$ 
A)  $x ^ { 2 } = 5$ 
B)  $5 ^ { x } = 2$ 
C)  $5 ^ { 2 } = x$ 
D)  $2 ^ { 5 } = x$

Question 6

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 5 x ^ { 2 } + 1 , g ( x ) = \sqrt { \frac { x - 1 } { 5 } }$$

Accepted Answer

A)  Yes; Exclude the interval $( - \infty , 1 )$ 
B)  No 
C)  Yes; No values need to be excluded. 
D)  Yes; Exclude the interval $( - \infty , 5 )$ 
A)  Yes; Exclude the interval $( - \infty , 1 )$ 
B)  No 
C)  Yes; No values need to be excluded. 
D)  Yes; Exclude the interval $( - \infty , 5 )$

Question 7

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.
-$\log _ { 4 } 71.14$

Accepted Answer

A)  $17.785$ 
B)  $0.325$ 
C)  $3.076$ 
D)  $1.852$ 
A)  $17.785$ 
B)  $0.325$ 
C)  $3.076$ 
D)  $1.852$

Question 8

Find the present value. Round to the nearest cent.
-To get $10,000 after 3 years at 6% compounded monthly

Accepted Answer

A)  $10,616.78 
B)  $8,356.45 
C)  $3,333.33 
D)  $9,419.05 
A)  $10,616.78 
B)  $8,356.45 
C)  $3,333.33 
D)  $9,419.05

Question 9

Write the word or phrase that best completes each statement or answers the question.
-Find the magnitude (to one decimal place) of an earthquake whose seismographic reading is 2000 millimeters at
a distance of 100 kilometers from its epicenter.

Accepted Answer

The magnitude of the

Question 10

The function f is one-to-one. Find its inverse.
-$$f ( x ) = 2 x + 8$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x + 8 } { 2 }$ 
B)  $f ( x ) = \frac { x - 8 } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { x + 2 } { 8 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 8 } { 2 }$ 
A)  $f ^ { - 1 } ( x ) = \frac { x + 8 } { 2 }$ 
B)  $f ( x ) = \frac { x - 8 } { 2 }$ 
C)  $f ^ { - 1 } ( x ) = - \frac { x + 2 } { 8 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 8 } { 2 }$

Question 11

Solve the problem.
-Find a so that the graph of $f ( x ) = \log _ { a } x$ contains the point $( 4,10 )$.

Accepted Answer

A)  $\frac { 5 } { 2 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  $\sqrt [ 10 ] { 4 }$ 
D)  $\sqrt [ 4 ] { 10 }$ 
A)  $\frac { 5 } { 2 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  $\sqrt [ 10 ] { 4 }$ 
D)  $\sqrt [ 4 ] { 10 }$

Question 12

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve.
-$f(x)=\sqrt{x+2}$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 13

Approximate the value using a calculator. Express answer rounded to three decimal places.
-$2.9 \pi$

Accepted Answer

A)  $9.111$ 
B)  $36.462$ 
C)  $28.357$ 
D)  $27.652$ 
A)  $9.111$ 
B)  $36.462$ 
C)  $28.357$ 
D)  $27.652$

Question 14

Decide whether the composite functions, f ° g and g ° f, are equal to x.
-$$f ( x ) = \sqrt [ 5 ] { x - 8 } , g ( x ) = x ^ { 5 } + 8$$

Accepted Answer

A)  Yes, yes 
B)  Yes, no 
C)  No, no 
D)  No, yes 
A)  Yes, yes 
B)  Yes, no 
C)  No, no 
D)  No, yes

Question 15

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of
the inverse.
-$$f ( x ) = \frac { 3 } { x - 1 }$$

Accepted Answer

A)  $f ( x ) : D = \{ x \mid x \neq - 3 \} , R = \{ y \mid y \neq 1 \}$
$$f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 1 \} , R = \{ y \mid y \neq - 3 \}$$ 
B)  $f ( x )$ : D is all real numbers, $R = \{ y | y \neq - 3 \rangle$; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } z - 3 \} , \mathrm { R }$ is all real numbers 
C)  $f ( x ) : D = \{ x \mid x \neq 1 \} , R = \{ y \neq 0 \}$; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq 0 \} , \mathrm { R } = \{ \mathrm { y } \mid \mathrm { y } \neq 1 \}$ 
D)  $f ( x )$ : D is all real numbers, $R$ is all real numbers; $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ : $\mathrm { D }$ is all real numbers, $\mathrm { R }$ is all real numbers 
A)  $f ( x ) : D = \{ x \mid x \neq - 3 \} , R = \{ y \mid y \neq 1 \}$
$$f ^ { - 1 } ( x ) : D = \{ x \mid x \neq 1 \} , R = \{ y \mid y \neq - 3 \}$$ 
B)  $f ( x )$ : D is all real numbers, $R = \{ y | y \neq - 3 \rangle$; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } z - 3 \} , \mathrm { R }$ is all real numbers 
C)  $f ( x ) : D = \{ x \mid x \neq 1 \} , R = \{ y \neq 0 \}$; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) : \mathrm { D } = \{ \mathrm { x } \mid \mathrm { x } \neq 0 \} , \mathrm { R } = \{ \mathrm { y } \mid \mathrm { y } \neq 1 \}$ 
D)  $f ( x )$ : D is all real numbers, $R$ is all real numbers; $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ : $\mathrm { D }$ is all real numbers, $\mathrm { R }$ is all real numbers

Question 16

Choose the one alternative that best completes the statement or answers the question.
-The logistic growth model $\mathrm { P } ( \mathrm { t } ) = \frac { 1 } { 1 + 6.69 \mathrm { e } ^ { - 0.753 \mathrm { t } } }$ represents the proportion of the total market of a new product as it penetrates the market t years after introduction. When will the product have $65 \%$ of the market?

Accepted Answer

A)  $2.95$ years 
B)  $3.35$ years 
C)  $4.35$ years 
D)  $1.95$ years 
A)  $2.95$ years 
B)  $3.35$ years 
C)  $4.35$ years 
D)  $1.95$ years

Question 17

Choose the one alternative that best completes the statement or answers the question.
The graph of a logarithmic function is shown. Select the function which matches the graph.
-

Accepted Answer

A)  $f ( x ) = - \log _ { 3 } x$ 
B)  $f ( x ) = 1 - \log _ { 3 } x$ 
C)  $f ( x ) = \log _ { 3 } ( - x )$ 
D)  $f ( x ) = \log _ { 3 } x$ 
A)  $f ( x ) = - \log _ { 3 } x$ 
B)  $f ( x ) = 1 - \log _ { 3 } x$ 
C)  $f ( x ) = \log _ { 3 } ( - x )$ 
D)  $f ( x ) = \log _ { 3 } x$

Question 18

Write the word or phrase that best completes each statement or answers the question.
-A venture capital firm invested $2,000,000 in a new company in 1995. In 1999, they sold their stake in the
company for $10,500,000. What was the average annual rate of return on their investment?

Accepted Answer

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

Question 19

Find the domain of the function.
-$$f ( x ) = \ln \left( \frac { 1 } { x - 9 } \right)$$

Accepted Answer

A)  $x > 1$ 
B)  $x > 0$ 
C)  $x > - 9$ 
D)  $x > 9$ 
A)  $x > 1$ 
B)  $x > 0$ 
C)  $x > - 9$ 
D)  $x > 9$

Question 20

Write the word or phrase that best completes each statement or answers the question.
-If $5,000 is invested for 6 years at 5%, compounded continuously, find the future value.

Accepted Answer

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

Use the horizontal line test to determine whether the function is one-to-one. -

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 5 } x = 2$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 5 x ^ { 2 } + 1 , g ( x ) = \sqrt { \frac { x - 1 } { 5 } }$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { 4 } 71.14$

Find the present value. Round to the nearest cent. -To get $10,000 after 3 years at 6% compounded monthly

Write the word or phrase that best completes each statement or answers the question. -Find the magnitude (to one decimal place) of an earthquake whose seismographic reading is 2000 millimeters at a distance of 100 kilometers from its epicenter.

The function f is one-to-one. Find its inverse. - $f ( x ) = 2 x + 8$

Solve the problem. -Find a so that the graph of $f ( x ) = \log _ { a } x$ contains the point $( 4,10 )$ .

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - $f(x)=\sqrt{x+2}$ $The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - f(x)=\sqrt{x+2}$

Approximate the value using a calculator. Express answer rounded to three decimal places. - $2.9 \pi$

Decide whether the composite functions, f ° g and g ° f, are equal to x. - $f ( x ) = \sqrt [ 5 ] { x - 8 } , g ( x ) = x ^ { 5 } + 8$

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. - $f ( x ) = \frac { 3 } { x - 1 }$

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Write the word or phrase that best completes each statement or answers the question. -A venture capital firm invested $2,000,000 in a new company in 1995. In 1999, they sold their stake in the company for $10,500,000. What was the average annual rate of return on their investment?

Find the domain of the function. - $f ( x ) = \ln \left( \frac { 1 } { x - 9 } \right)$

Write the word or phrase that best completes each statement or answers the question. -If $5,000 is invested for 6 years at 5%, compounded continuously, find the future value.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 4: Exponential and Logarithmic Functions

Use the horizontal line test to determine whether the function is one-to-one. -

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Change the logarithmic expression to an equivalent expression involving an exponent. - log⁡5x=2\log _ { 5 } x = 2log5​x=2

Decide whether or not the functions are inverses of each other. - f(x)=5x2+1,g(x)=x−15f ( x ) = 5 x ^ { 2 } + 1 , g ( x ) = \sqrt { \frac { x - 1 } { 5 } }f(x)=5x2+1,g(x)=5x−1​​

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - log⁡471.14\log _ { 4 } 71.14log4​71.14

Find the present value. Round to the nearest cent. -To get $10,000 after 3 years at 6% compounded monthly

Write the word or phrase that best completes each statement or answers the question. -Find the magnitude (to one decimal place) of an earthquake whose seismographic reading is 2000 millimeters at a distance of 100 kilometers from its epicenter.

The function f is one-to-one. Find its inverse. - f(x)=2x+8f ( x ) = 2 x + 8f(x)=2x+8

Solve the problem. -Find a so that the graph of f(x)=log⁡axf ( x ) = \log _ { a } xf(x)=loga​x contains the point (4,10)( 4,10 )(4,10) .

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - f(x)=x+2f(x)=\sqrt{x+2}f(x)=x+2​

Approximate the value using a calculator. Express answer rounded to three decimal places. - 2.9π2.9 \pi2.9π

Decide whether the composite functions, f ° g and g ° f, are equal to x. - f(x)=x−85,g(x)=x5+8f ( x ) = \sqrt [ 5 ] { x - 8 } , g ( x ) = x ^ { 5 } + 8f(x)=5x−8​,g(x)=x5+8

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. - f(x)=3x−1f ( x ) = \frac { 3 } { x - 1 }f(x)=x−13​

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Write the word or phrase that best completes each statement or answers the question. -A venture capital firm invested $2,000,000 in a new company in 1995. In 1999, they sold their stake in the company for $10,500,000. What was the average annual rate of return on their investment?

Find the domain of the function. - f(x)=ln⁡(1x−9)f ( x ) = \ln \left( \frac { 1 } { x - 9 } \right)f(x)=ln(x−91​)

Write the word or phrase that best completes each statement or answers the question. -If $5,000 is invested for 6 years at 5%, compounded continuously, find the future value.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 5 } x = 2$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 5 x ^ { 2 } + 1 , g ( x ) = \sqrt { \frac { x - 1 } { 5 } }$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { 4 } 71.14$

The function f is one-to-one. Find its inverse. - $f ( x ) = 2 x + 8$

Solve the problem. -Find a so that the graph of $f ( x ) = \log _ { a } x$ contains the point $( 4,10 )$ .

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - $f(x)=\sqrt{x+2}$ $The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - f(x)=\sqrt{x+2}$

Approximate the value using a calculator. Express answer rounded to three decimal places. - $2.9 \pi$

Decide whether the composite functions, f ° g and g ° f, are equal to x. - $f ( x ) = \sqrt [ 5 ] { x - 8 } , g ( x ) = x ^ { 5 } + 8$

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. - $f ( x ) = \frac { 3 } { x - 1 }$

Find the domain of the function. - $f ( x ) = \ln \left( \frac { 1 } { x - 9 } \right)$