Question 1

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$\log _ { 3 } ( x + 1 ) = - 2$

Accepted Answer

A)  $\left\{ \frac { 10 } { 9 } \right\}$ 
B)  $\left\{ - \frac { 8 } { 9 } \right\}$ 
C)  $\{ - 1 \rangle$ 
D)  $\left\{ \frac { 5 } { 4 } \right\}$ 
A)  $\left\{ \frac { 10 } { 9 } \right\}$ 
B)  $\left\{ - \frac { 8 } { 9 } \right\}$ 
C)  $\{ - 1 \rangle$ 
D)  $\left\{ \frac { 5 } { 4 } \right\}$

Question 2

Write the word or phrase that best completes each statement or answers the question.
-The formula $$\mathrm { D } = 8 \mathrm { e } ^ { - 0.6 \mathrm {~h} }$$ can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug
has been administered. The drug is to be administered again when the amount in the bloodstream reaches 4 milligrams.
What is the time between injections?

Accepted Answer

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

Question 3

For the given functions f and g, find the requested composite function.
-$f ( x ) = \frac { 7 } { x - 3 } , \quad g ( x ) = \frac { 2 } { 5 x } ; \quad$ Find $( f \circ g ) ( x )$

Accepted Answer

A)  $\frac { 35 x } { 2 - 15 x }$ 
B)  $\frac { 7 x } { 2 - 15 x }$ 
C)  $\frac { 2 x - 6 } { 35 x }$ 
D)  $\frac { 35 x } { 2 + 15 x }$ 
A)  $\frac { 35 x } { 2 - 15 x }$ 
B)  $\frac { 7 x } { 2 - 15 x }$ 
C)  $\frac { 2 x - 6 } { 35 x }$ 
D)  $\frac { 35 x } { 2 + 15 x }$

Question 4

Find the present value. Round to the nearest cent.
-To get $6500 after 6 years at 7% compounded quarterly

Accepted Answer

A)  $2,213.65 
B)  $4,331.22 
C)  $4,361.36 
D)  $4,286.35 
A)  $2,213.65 
B)  $4,331.22 
C)  $4,361.36 
D)  $4,286.35

Question 5

Decide whether the composite functions, f ° g and g ° f, are equal to x.
-$$f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$$

Accepted Answer

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

Question 6

Find the domain of the function.
-$$f ( x ) = \ln \left( 6 x - x ^ { 2 } \right)$$

Accepted Answer

A)  $x \leq 6$ 
B)  $- 6 < x < 6$ 
C)  $- 6 \leq x < 0$ 
D)  $0 < x < 6$ 
A)  $x \leq 6$ 
B)  $- 6 < x < 6$ 
C)  $- 6 \leq x < 0$ 
D)  $0 < x < 6$

Question 7

Solve the equation.
-$$\left( e ^ { x } \right) ^ { x } \cdot e ^ { 54 } = e ^ { 15 x }$$

Accepted Answer

A)  $\{ 6,9 \}$ 
B)  $\{ 9 \}$ 
C)  $\{ 6 \}$ 
D)  $\{ - 6 , - 9 \}$ 
A)  $\{ 6,9 \}$ 
B)  $\{ 9 \}$ 
C)  $\{ 6 \}$ 
D)  $\{ - 6 , - 9 \}$

Question 8

The function f is one-to-one. Find its inverse.
-$$f ( x ) = \frac { 6 } { x }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = - 6 x$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 } { \mathrm { x } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 6 \mathrm { x }$ 
A)  $f ^ { - 1 } ( x ) = \frac { x } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = - 6 x$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 } { \mathrm { x } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 6 \mathrm { x }$

Question 9

Change the logarithmic expression to an equivalent expression involving an exponent.
-$$\log _ { b } 49 = \frac { 2 } { 3 }$$

Accepted Answer

A)  $b ^ { 3 / 2 } = 49$ 
B)  $\left( \frac { 2 } { 3 } \right) ^ { b } = 49$ 
C)  $49 ^ { 2 / 3 } = b$ 
D)  $b ^ { 2 / 3 } = 49$ 
A)  $b ^ { 3 / 2 } = 49$ 
B)  $\left( \frac { 2 } { 3 } \right) ^ { b } = 49$ 
C)  $49 ^ { 2 / 3 } = b$ 
D)  $b ^ { 2 / 3 } = 49$

Question 10

Choose the one alternative that best completes the statement or answers the question.
The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this
function $$M ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) , \text { where } x _ { 0 } = 10 ^ { - 3 } .$$
-What is the magnitude of an earthquake whose seismographic reading is 7.6 millimeters at a distance of 100 kilometers from its epicenter?

Accepted Answer

A)  0.38808 
B)  0.20281 
C)  3.8808 
D)  2.0281 
A)  0.38808 
B)  0.20281 
C)  3.8808 
D)  2.0281

Question 11

Choose the one alternative that best completes the statement or answers the question.
-A thermometer reading $84 ^ { \circ } \mathrm { F }$ is placed inside a cold storage room with a constant temperature of $38 ^ { \circ } \mathrm { F }$. If the thermometer reads $77 ^ { \circ } \mathrm { F }$ in 11 minutes, how long before it reaches $56 ^ { \circ } \mathrm { F }$ ? Assume the cooling follows Newton's L of Cooling:
$$\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } } .$$
(Round your answer to the nearest whole minute.)

Accepted Answer

A)  $- 20$ minutes 
B)  22 minutes 
C)  4 minutes 
D)  63 minutes 
A)  $- 20$ minutes 
B)  22 minutes 
C)  4 minutes 
D)  63 minutes

Question 12

Graph the function.
-$$\begin{array}{l}
f ( x ) = 5 | x |\

\end{array}$$

Accepted Answer

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

Question 13

Choose the one alternative that best completes the statement or answers the question.
-$$\ln \frac { 1 } { \mathrm { e } ^ { 5 } } = - 5$$

Accepted Answer

A)  $\left( \frac { 1 } { \mathrm { e } ^ { 5 } } \right) ^ { - 5 } = \mathrm { e }$ 
B)  $\left( \frac { 1 } { e ^ { 5 } } \right) ^ { e } = - 5$ 
C)  $\mathrm { e } ^ { - 5 } = \frac { 1 } { \mathrm { e } ^ { 5 } }$ 
D)  $- 5 ^ { \mathrm { e } } = \frac { 1 } { \mathrm { e } ^ { 5 } }$ 
A)  $\left( \frac { 1 } { \mathrm { e } ^ { 5 } } \right) ^ { - 5 } = \mathrm { e }$ 
B)  $\left( \frac { 1 } { e ^ { 5 } } \right) ^ { e } = - 5$ 
C)  $\mathrm { e } ^ { - 5 } = \frac { 1 } { \mathrm { e } ^ { 5 } }$ 
D)  $- 5 ^ { \mathrm { e } } = \frac { 1 } { \mathrm { e } ^ { 5 } }$

Question 14

Choose the one alternative that best completes the statement or answers the question.
-The logistic growth function $\mathrm { f } ( \mathrm { t } ) = \frac { 50,000 } { 1 + 2,499.0 \mathrm { e } ^ { - 1.9 t } }$ models the number of people who have become ill with a particular infection $t$ weeks after its initial outbreak in a particular community. How many people became ill with this infection when the epidemic began?

Accepted Answer

A)  20 people 
B)  2,500 people 
C)  50,000 people 
D)  2,499 people 
A)  20 people 
B)  2,500 people 
C)  50,000 people 
D)  2,499 people

Question 15

The function f is one-to-one. Find its inverse.
-$$f ( x ) = ( x + 7 ) ^ { 3 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 7$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 343$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } - 7$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 7$ 
A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 7$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 343$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } - 7$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 7$

Question 16

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.
-$f(x)=2^{-x}+5$

Accepted Answer

A)  domain of $f : ( - \infty , \infty )$; range of $f : ( 2 , \infty )$
horizontal asymptote: $\mathrm { y } = 2$

B)  domain of $\mathrm { f: } ( - \infty , \infty )$; range of $\mathrm { f } : ( 5 , \infty )$  horizontal asymptote: $\mathrm { y } = 5$
  
C)  domain of $\mathrm { f } : ( - \infty , \infty )$; range of $\mathrm { f } : ( 2 , \infty )$
 horizontal asymptote: $\mathrm { y } = 2$

D)  domain of $f : ( - \infty , \infty )$; range of $f : ( 5 , \infty )$ horizontal asymptote: $y = 5$
  
A)  domain of $f : ( - \infty , \infty )$; range of $f : ( 2 , \infty )$
horizontal asymptote: $\mathrm { y } = 2$

B)  domain of $\mathrm { f: } ( - \infty , \infty )$; range of $\mathrm { f } : ( 5 , \infty )$  horizontal asymptote: $\mathrm { y } = 5$
  
C)  domain of $\mathrm { f } : ( - \infty , \infty )$; range of $\mathrm { f } : ( 2 , \infty )$
 horizontal asymptote: $\mathrm { y } = 2$

D)  domain of $f : ( - \infty , \infty )$; range of $f : ( 5 , \infty )$ horizontal asymptote: $y = 5$

Question 17

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$\log _ { 5 } 25 = x$$

Accepted Answer

A)  $\{ 5 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ 30 \}$ 
D)  $\{ 125 \}$ 
A)  $\{ 5 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ 30 \}$ 
D)  $\{ 125 \}$

Question 18

Choose the one alternative that best completes the statement or answers the question.
The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this
function $$M ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) , \text { where } x _ { 0 } = 10 ^ { - 3 } .$$
-What is the magnitude of an earthquake whose seismographic reading is 6.6 millimeters at a distance of 100 kilometers from its epicenter? Round the answer to the nearest tenth.

Accepted Answer

A)  2.8 
B)  3.8 
C)  2.5 
D)  819.5 
A)  2.8 
B)  3.8 
C)  2.5 
D)  819.5

Question 19

Choose the one alternative that best completes the statement or answers the question.
-In a Psychology class, the students were tested at the end of the course on a final exam. Then they were retested with an equivalent test at subsequent time intervals. Their average scores after t months are given in the table.
$\begin{array}{l|ccccc}
\text { Time, } \text { (in months) } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Score, } \mathrm{y} \text { (in percentage) } & 86.2 & 85.7 & 85.4 & 85.2 & 85.0
\end{array}$
 Using a graphing utility, fit a logarithmic function $y = a + b \ln x$ to the data. Using the function you found, estin how long will it take for the test scores to fall below $84 \%$. Express your answer to the nearest month.

Accepted Answer

A)  8 months 
B)  12 months 
C)  20 months 
D)  10 months 
A)  8 months 
B)  12 months 
C)  20 months 
D)  10 months

Question 20

Write as the sum and/or difference of logarithms. Express powers as factors.
-$\log _ { 3 } \left( \frac { \sqrt { x } } { 27 } \right)$

Accepted Answer

A)  $9 - \frac { 1 } { 2 } \log _ { 3 } x$ 
B)  $- 3 \log _ { 3 } x$ 
C)  $\log _ { 3 } x - 3$ 
D)  $\frac { 1 } { 2 } \log _ { 3 } x - 3$ 
A)  $9 - \frac { 1 } { 2 } \log _ { 3 } x$ 
B)  $- 3 \log _ { 3 } x$ 
C)  $\log _ { 3 } x - 3$ 
D)  $\frac { 1 } { 2 } \log _ { 3 } x - 3$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\log _ { 3 } ( x + 1 ) = - 2$

For the given functions f and g, find the requested composite function. - $f ( x ) = \frac { 7 } { x - 3 } , \quad g ( x ) = \frac { 2 } { 5 x } ; \quad$ Find $( f \circ g ) ( x )$

Find the present value. Round to the nearest cent. -To get $6500 after 6 years at 7% compounded quarterly

Decide whether the composite functions, f ° g and g ° f, are equal to x. - $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$

Find the domain of the function. - $f ( x ) = \ln \left( 6 x - x ^ { 2 } \right)$

Solve the equation. - $\left( e ^ { x } \right) ^ { x } \cdot e ^ { 54 } = e ^ { 15 x }$

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 6 } { x }$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { b } 49 = \frac { 2 } { 3 }$

Graph the function. - f(x)=5|x| $Graph the function. - \begin{array}{l} f ( x ) = 5 | x |\\ \end{array}$

Choose the one alternative that best completes the statement or answers the question. - $\ln \frac { 1 } { \mathrm { e } ^ { 5 } } = - 5$

The function f is one-to-one. Find its inverse. - $f ( x ) = ( x + 7 ) ^ { 3 }$

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - $f(x)=2^{-x}+5$ $Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - f(x)=2^{-x}+5$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\log _ { 5 } 25 = x$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 3 } \left( \frac { \sqrt { x } } { 27 } \right)$

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

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - log⁡3(x+1)=−2\log _ { 3 } ( x + 1 ) = - 2log3​(x+1)=−2

For the given functions f and g, find the requested composite function. - f(x)=7x−3,g(x)=25x;f ( x ) = \frac { 7 } { x - 3 } , \quad g ( x ) = \frac { 2 } { 5 x } ; \quadf(x)=x−37​,g(x)=5x2​; Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)