Question 1

Find the domain of the function.
-$$f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 16 x + 63 \right)$$

Accepted Answer

A)  $( 9 , \infty )$ 
B)  $( - \infty , 7 ) \cup ( 9 , \infty )$ 
C)  $( - 7,9 )$ 
D)  $( - \infty , - 7 )$ 
A)  $( 9 , \infty )$ 
B)  $( - \infty , 7 ) \cup ( 9 , \infty )$ 
C)  $( - 7,9 )$ 
D)  $( - \infty , - 7 )$

Question 2

Evaluate the expression using the values given in the table.
-$( \mathrm { f\circ g })( 3 )$
$\begin{array}{c|r|r|r|r}
\mathrm{x} & 1 & 7 & 10 & 12 \
\hline \mathrm{f}(\mathrm{x}) & -2 & 10 & 0 & 12
\end{array}$

$\begin{array}{c|r|r|r|r}
\mathrm{x} & -5 & -2 & 1 & 3 \
\hline \mathrm{g}(\mathrm{x}) & 1 & -7 & 7 & 10
\end{array}$

Accepted Answer

A)  Undefined 
B)  10 
C)  7 
D)  0 
A)  Undefined 
B)  10 
C)  7 
D)  0

Question 3

Choose the one alternative that best completes the statement or answers the question.
Find the domain of the composite function f ° g.
-$f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10$

Accepted Answer

A)  $\{ x \mid x \geq 0 \}$ 
B)  $\{ x \mid x \leq - 2$ or $x \geq 0 \}$ 
C)  $\{ x \mid x \geq - 2 \}$ 
D)  $\{ x \mid x$ is any real number $\}$ 
A)  $\{ x \mid x \geq 0 \}$ 
B)  $\{ x \mid x \leq - 2$ or $x \geq 0 \}$ 
C)  $\{ x \mid x \geq - 2 \}$ 
D)  $\{ x \mid x$ is any real number $\}$

Question 4

Find the exact value of the logarithmic expression.
-$\log _ { 10 } 1,000$

Accepted Answer

A)  30 
B)  $- 3$ 
C)  $\frac { 1 } { 1000 }$ 
D)  3 
A)  30 
B)  $- 3$ 
C)  $\frac { 1 } { 1000 }$ 
D)  3

Question 5

Choose the one alternative that best completes the statement or answers the question.
-If $3 ^ { - x } = \frac { 1 } { 5 }$, what does $9 ^ { x }$ equal?

Accepted Answer

A)  $- 25$ 
B)  5 
C)  25 
D)  $\frac { 1 } { 25 }$ 
A)  $- 25$ 
B)  5 
C)  25 
D)  $\frac { 1 } { 25 }$

Question 6

Evaluate the expression using the graphs of y = f(x) and y = g(x).
-Evaluate $( \mathrm { fg } ) ( - 1 )$

Accepted Answer

A)  0 
B)  $- 2$ 
C)  3 
D)  $- 1$ 
A)  0 
B)  $- 2$ 
C)  3 
D)  $- 1$

Question 7

Choose the one alternative that best completes the statement or answers the question.
-$\ln \left( \frac { ( x + 5 ) ( x - 2 ) } { ( x - 8 ) ^ { 4 } } \right) ^ { 4 / 3 } , \quad x > 2$

Accepted Answer

A)  $4 \ln ( x + 5 ) - 3 \ln ( x - 2 ) - \frac { 16 } { 3 } \ln ( x - 8 )$ 
B)  $\frac { 4 } { 3 } \ln \left( x ^ { 2 } + 7 x - 10 \right) - \frac { 16 } { 3 } \ln ( x - 8 )$ 
C)  $\ln ( x + 5 ) + \ln ( x - 2 ) + \ln 4 - 16 \ln ( x - 8 ) - \ln 3$ 
D)  $\frac { 4 } { 3 } \ln ( x + 5 ) + \frac { 4 } { 3 } \ln ( x - 2 ) - \frac { 16 } { 3 } \ln ( x - 8 )$ 
A)  $4 \ln ( x + 5 ) - 3 \ln ( x - 2 ) - \frac { 16 } { 3 } \ln ( x - 8 )$ 
B)  $\frac { 4 } { 3 } \ln \left( x ^ { 2 } + 7 x - 10 \right) - \frac { 16 } { 3 } \ln ( x - 8 )$ 
C)  $\ln ( x + 5 ) + \ln ( x - 2 ) + \ln 4 - 16 \ln ( x - 8 ) - \ln 3$ 
D)  $\frac { 4 } { 3 } \ln ( x + 5 ) + \frac { 4 } { 3 } \ln ( x - 2 ) - \frac { 16 } { 3 } \ln ( x - 8 )$

Question 8

For the given functions f and g, find the requested composite function.
-$f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 8 x - 6$
Find $( f \circ g ) ( x )$.

Accepted Answer

A)  $8 \sqrt { x - 4 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $8 \sqrt { x + 2 } - 6$ 
D)  $2 \sqrt { 2 x + 1 }$ 
A)  $8 \sqrt { x - 4 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $8 \sqrt { x + 2 } - 6$ 
D)  $2 \sqrt { 2 x + 1 }$

Question 9

Choose the one alternative that best completes the statement or answers the question.
-The functio models the amount in pounds of a particular radioactive material stored in a $$\mathrm { A } = \mathrm { A } _ { \mathrm { O } } \mathrm { e } ^ { - 0.0099 \mathrm { x } }$$ concrete vault, where x is the number of years since the material was put into the vault. If 500 pounds of the material are initially put into the vault, how many pounds will be left after 80 years?

Accepted Answer

A)  286 pounds 
B)  273 pounds 
C)  226 pounds 
D)  219 pounds 
A)  286 pounds 
B)  273 pounds 
C)  226 pounds 
D)  219 pounds

Question 10

The graph of an exponential function is given. Match the graph to one of the following functions.
-

Accepted Answer

A)  $y = 0.65 ^ { x }$ 
B)  $y = 0.32 ^ { x }$ 
C)  $y = 2.4 ^ { x }$ 
D)  $y = 3.5 ^ { x }$ 
A)  $y = 0.65 ^ { x }$ 
B)  $y = 0.32 ^ { x }$ 
C)  $y = 2.4 ^ { x }$ 
D)  $y = 3.5 ^ { x }$

Question 11

Solve the equation.
-$$3 ^ { ( 3 x - 6 ) } = 27$$

Accepted Answer

A)  $\{ 9 \}$ 
B)  $\{ - 3 \}$ 
C)  $\left\{ \frac { 1 } { 9 } \right\}$ 
D)  $\{ 3 \}$ 
A)  $\{ 9 \}$ 
B)  $\{ - 3 \}$ 
C)  $\left\{ \frac { 1 } { 9 } \right\}$ 
D)  $\{ 3 \}$

Question 12

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = \frac { 6 + x } { x } , g ( x ) = \frac { 6 } { x - 1 }$$

Accepted Answer

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

Question 13

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

Accepted Answer

A)  $3 x + 4$ 
B)  $x + 4$ 
C)  $x - \frac { 2 } { 3 }$ 
D)  $x$ 
A)  $3 x + 4$ 
B)  $x + 4$ 
C)  $x - \frac { 2 } { 3 }$ 
D)  $x$

Question 14

Write the word or phrase that best completes each statement or answers the question.
-Two earthquakes differ by 0.1 when measured on the Richter scale. How would the seismographic readings
differ at a distance of 100 kilometers from the epicenter?

Accepted Answer

The earthquake of greater magn

Question 15

Solve the equation.
-$$3 ^ { x } = \frac { 1 } { 27 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 3 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$ 
A)  $\left\{ \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 3 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$

Question 16

Approximate the value using a calculator. Express answer rounded to three decimal places.
-$\mathrm { e } ^ { - 2.7 }$

Accepted Answer

A)  $0.367$ 
B)  $0.067$ 
C)  $- 0.067$ 
D)  $- 7.339$ 
A)  $0.367$ 
B)  $0.067$ 
C)  $- 0.067$ 
D)  $- 7.339$

Question 17

Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$4 ^ { x + 4 } = 5 ^ { 2 x + 5 }$$

Accepted Answer

A)  $\{ 7 \ln 5 - 5 \ln 4 \}$ 
B)  $\{ \ln 5 - \ln 4 \}$ 
C)  $\left\{ \frac { 5 \ln 5 - 4 \ln 4 } { \ln 4 - 2 \ln 5 } \right\}$ 
D)  $\left\{ \ln \left[ \frac { 5 ^ { 5 } } { 4 ^ { 4 } } - \frac { 4 } { 5 ^ { 2 } } \right] \right\}$ 
A)  $\{ 7 \ln 5 - 5 \ln 4 \}$ 
B)  $\{ \ln 5 - \ln 4 \}$ 
C)  $\left\{ \frac { 5 \ln 5 - 4 \ln 4 } { \ln 4 - 2 \ln 5 } \right\}$ 
D)  $\left\{ \ln \left[ \frac { 5 ^ { 5 } } { 4 ^ { 4 } } - \frac { 4 } { 5 ^ { 2 } } \right] \right\}$

Question 18

Graph the function.
-$f(x)=-1+e^{X}$

Accepted Answer

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

Question 19

Choose the one alternative that best completes the statement or answers the question.
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$$4^{ ( x - 1 )} = 19$$

Accepted Answer

A)  $\{ 5.75 \}$ 
B)  $\{ 3.12 \}$ 
C)  $\{ 1.12 \}$ 
D)  $\{ 2.26 \}$ 
A)  $\{ 5.75 \}$ 
B)  $\{ 3.12 \}$ 
C)  $\{ 1.12 \}$ 
D)  $\{ 2.26 \}$

Question 20

Choose the one alternative that best completes the statement or answers the question.
-A cup of coffee is heated to $194 ^ { \circ }$ and is then allowed to cool in a room whose air temperature is $72 ^ { \circ }$. After 11 minutes, the temperature of the cup of coffee is $140 ^ { \circ }$. Find the time needed for the coffee to cool to a temperature of $102 ^ { \circ }$. Assume the cooling follows Newton's Law of Cooling:
$$\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } } \text {. }$$
(Round your answer to one decimal place.)

Accepted Answer

A)  $15.1$ minutes 
B)  $29.7$ minutes 
C)  $41.1$ minutes 
D)  $26.4$ minutes 
A)  $15.1$ minutes 
B)  $29.7$ minutes 
C)  $41.1$ minutes 
D)  $26.4$ minutes

Find the domain of the function. - $f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 16 x + 63 \right)$

Evaluate the expression using the values given in the table. - $( \mathrm { f\circ g })( 3 )$ 1 7 10 12 () -2 10 0 12 -5 -2 1 3 () 1 -7 7 10

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10$

Find the exact value of the logarithmic expression. - $\log _ { 10 } 1,000$

Choose the one alternative that best completes the statement or answers the question. -If $3 ^ { - x } = \frac { 1 } { 5 }$ , what does $9 ^ { x }$ equal?

Evaluate the expression using the graphs of y = f(x) and y = g(x). -Evaluate $( \mathrm { fg } ) ( - 1 )$ $Evaluate the expression using the graphs of y = f(x) and y = g(x). -Evaluate ( \mathrm { fg } ) ( - 1 )$

Choose the one alternative that best completes the statement or answers the question. - $\ln \left( \frac { ( x + 5 ) ( x - 2 ) } { ( x - 8 ) ^ { 4 } } \right) ^ { 4 / 3 } , \quad x > 2$

For the given functions f and g, find the requested composite function. - $f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 8 x - 6$ Find $( f \circ g ) ( x )$ .

The graph of an exponential function is given. Match the graph to one of the following functions. -

Solve the equation. - $3 ^ { ( 3 x - 6 ) } = 27$

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 6 + x } { x } , g ( x ) = \frac { 6 } { x - 1 }$

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

Write the word or phrase that best completes each statement or answers the question. -Two earthquakes differ by 0.1 when measured on the Richter scale. How would the seismographic readings differ at a distance of 100 kilometers from the epicenter?

Solve the equation. - $3 ^ { x } = \frac { 1 } { 27 }$

Approximate the value using a calculator. Express answer rounded to three decimal places. - $\mathrm { e } ^ { - 2.7 }$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $4 ^ { x + 4 } = 5 ^ { 2 x + 5 }$

Graph the function. - $f(x)=-1+e^{X}$ $Graph the function. - f(x)=-1+e^{X}$

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $4^{ ( x - 1 )} = 19$

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

Find the domain of the function. - f(x)=log⁡10(x2−16x+63)f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 16 x + 63 \right)f(x)=log10​(x2−16x+63)

Evaluate the expression using the values given in the table. - (f∘g)(3)( \mathrm { f\circ g })( 3 )(f∘g)(3) 1 7 10 12 () -2 10 0 12 -5 -2 1 3 () 1 -7 7 10

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - f(x)=x;g(x)=5x+10f ( x ) = \sqrt { x } ; \quad g ( x ) = 5 x + 10f(x)=x​;g(x)=5x+10

Find the exact value of the logarithmic expression. - log⁡101,000\log _ { 10 } 1,000log10​1,000

Choose the one alternative that best completes the statement or answers the question. -If 3−x=153 ^ { - x } = \frac { 1 } { 5 }3−x=51​ , what does 9x9 ^ { x }9x equal?

Evaluate the expression using the graphs of y = f(x) and y = g(x). -Evaluate (fg)(−1)( \mathrm { fg } ) ( - 1 )(fg)(−1)

Choose the one alternative that best completes the statement or answers the question. - ln⁡((x+5)(x−2)(x−8)4)4/3,x>2\ln \left( \frac { ( x + 5 ) ( x - 2 ) } { ( x - 8 ) ^ { 4 } } \right) ^ { 4 / 3 } , \quad x > 2ln((x−8)4(x+5)(x−2)​)4/3,x>2

For the given functions f and g, find the requested composite function. - f(x)=x+2,g(x)=8x−6f ( x ) = \sqrt { x + 2 } , \quad g ( x ) = 8 x - 6f(x)=x+2​,g(x)=8x−6 Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) .