Question 1

Indicate whether the function is one-to-one.
-{(5, 4), (6, 4), (7, 3), (8, -9)}

Accepted Answer

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

Question 2

The graph of a logarithmic function is shown. Select the function which matches the graph.
-  A) $y = \log ( x - 3 )$

Accepted Answer

B)  $y = \log ( 3 - x )$ 
C)  $y = 3 - \log ( x )$ 
D)  $y = \log ( x ) - 3$ 
B)  $y = \log ( 3 - x )$ 
C)  $y = 3 - \log ( x )$ 
D)  $y = \log ( x ) - 3$

Question 3

The graph of a logarithmic function is shown. Select the function which matches the graph.
-  A) $f ( x ) = \log _ { 3 } ( - x )$

Accepted Answer

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

Question 4

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$\log _ { 5 } 5 ^ { 4.71 }$

Accepted Answer

A)  $4.71$ 
B)  476 
C)  $0.212$ 
D)  5 
A)  $4.71$ 
B)  476 
C)  $0.212$ 
D)  5

Question 5

Express as a single logarithm.
-$3 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 2$

Accepted Answer

A)  $\log _ { a } 2 ( x + 1 )$ 
B)  $\log _ { a } ( 2 x + 1 ) + 2$ 
C)  $\log _ { a } ( 2 x + 3 )$ 
D)  $\log _ { a } \frac { a ^ { 2 } ( 2 x + 1 ) ^ { 3 } } { ( 2 x - 1 ) ^ { 2 } }$ 
A)  $\log _ { a } 2 ( x + 1 )$ 
B)  $\log _ { a } ( 2 x + 1 ) + 2$ 
C)  $\log _ { a } ( 2 x + 3 )$ 
D)  $\log _ { a } \frac { a ^ { 2 } ( 2 x + 1 ) ^ { 3 } } { ( 2 x - 1 ) ^ { 2 } }$

Question 6

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.
-$4 ^ { x + 7 } = 7$

Accepted Answer

A)  {1.56} 
B)  {-0.60} 
C)  {7.71} 
D)  {-5.60} 
A)  {1.56} 
B)  {-0.60} 
C)  {7.71} 
D)  {-5.60}

Question 7

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The accompanying tables represent a function f that converts seconds to hours and a function g that converts hours to days. $\begin{array}{r|rrrrr}
\mathrm{x} & 86,400 & 172,800 & 259,200 & 345,600 & 432,000 \
\hline \mathrm{f}(\mathrm{x}) & 24 & 48 & 72 & 96 & 120
\end{array}$

$\begin{array}{r|rrrrr}
\mathrm{x} & 24 & 48 & 72 & 96 & 120 \
\hline \mathrm{g}(\mathrm{x}) & 1 & 2 & 3 & 4 & 5
\end{array}$

Express $\left( \mathrm { f } ^ { - 1 } \mathrm { gg } ^ { - 1 } \right) ( \mathrm { x } )$ symbolically.

Accepted Answer

A)  $\left( f ^ { - 1 } g ^ { - 1 } \right) ( x ) = \frac { x } { 86,400 }$ 
B)  $\left( f ^ { - 1 } g ^ { - 1 } \right) ( x ) = \frac { x ^ { 2 } } { 86,400 }$ 
C)  $\left( f ^ { - 1 } g ^ { - 1 } \right) ( x ) = 86,400 x$ 
D)  $\left( \mathrm { f } ^ { - 1 } \mathrm { gg } ^ { - 1 } \right) ( \mathrm { x } ) = 86,400 \mathrm { x } ^ { 2 }$ 
A)  $\left( f ^ { - 1 } g ^ { - 1 } \right) ( x ) = \frac { x } { 86,400 }$ 
B)  $\left( f ^ { - 1 } g ^ { - 1 } \right) ( x ) = \frac { x ^ { 2 } } { 86,400 }$ 
C)  $\left( f ^ { - 1 } g ^ { - 1 } \right) ( x ) = 86,400 x$ 
D)  $\left( \mathrm { f } ^ { - 1 } \mathrm { gg } ^ { - 1 } \right) ( \mathrm { x } ) = 86,400 \mathrm { x } ^ { 2 }$

Question 8

Solve the problem.
-Between 7:00 AM and 8:00 AM, trains arrive at a subway station at a rate of 15 trains per hour (0.25 trains per minute). The following formula from statistics can be used to determine the probability that a train will arrive within t
Minutes of 7:00 AM. $$\mathrm { F } ( \mathrm { t } ) = 1 - \mathrm { e } ^ { - 0.25 \mathrm { t } }$$ Determine how many minutes are needed for the probability to reach 20%.

Accepted Answer

A)  0.89 min 
B)  2.35 min 
C)  5.34 min 
D)  4.12 min 
A)  0.89 min 
B)  2.35 min 
C)  5.34 min 
D)  4.12 min

Question 9

Solve the problem.
-The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $$y = 270 ( 2.7 ) ^ { 0.07 t }$$

Accepted Answer

A)  635 
B)  609 
C)  622 
D)  612 
A)  635 
B)  609 
C)  622 
D)  612

Question 10

Find the domain of the composite function f $f ^ { \circ } g $
-$$\mathrm { f } ( \mathrm { x } ) = 7 \mathrm { x } + 14 ; \quad \mathrm { g } ( \mathrm { x } ) = \mathrm { x } + 7$$

Accepted Answer

A)  $\{ x \mid x$ is any real number $\}$ 
B)  $\{ x \mid x \neq 9 \}$ 
C)  $\{ x \mid x \neq - 7 , x \neq - 2 \}$ 
D)  $\{ x \mid x \neq - 9 \}$ 
A)  $\{ x \mid x$ is any real number $\}$ 
B)  $\{ x \mid x \neq 9 \}$ 
C)  $\{ x \mid x \neq - 7 , x \neq - 2 \}$ 
D)  $\{ x \mid x \neq - 9 \}$

Question 11

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 12

Solve the equation.
-$$8 + 5 \ln x = 16$$

Accepted Answer

A)  $\left\{ e ^ { 8 / 5 } \right\}$ 
B)  $\left\{ \frac { 8 } { 5 \ln 1 } \right\}$ 
C)  $\left\{ \frac { e ^ { 8 } } { 5 } \right\}$ 
D)  $\left\{ \ln \left( \frac { 8 } { 5 } \right) \right\}$ 
A)  $\left\{ e ^ { 8 / 5 } \right\}$ 
B)  $\left\{ \frac { 8 } { 5 \ln 1 } \right\}$ 
C)  $\left\{ \frac { e ^ { 8 } } { 5 } \right\}$ 
D)  $\left\{ \ln \left( \frac { 8 } { 5 } \right) \right\}$

Question 13

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$\log _ { 4 } 4 ^ { - 15 }$

Accepted Answer

A)  $- 15$ 
B)  4 
C)  1 
D)  $- 60$ 
A)  $- 15$ 
B)  4 
C)  1 
D)  $- 60$

Question 14

The graph of a logarithmic function is shown. Select the function which matches the graph.
-  A) $y = \log ( x )$

Accepted Answer

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

Question 15

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 16

Solve the problem.
-The population of a particular country was 30 million in 1984; in 1995, it was 34 million. The exponential growth function $\mathrm { A } = 30 \mathrm { e } ^ { \mathrm { kt } }$ describes the population of this country t years after 1984. Use the fact that 11 years
After 1984 the population increased by 4 million to find k to three decimal places.

Accepted Answer

A)  0.126 
B)  0.011 
C)  0.630 
D)  0.021 
A)  0.126 
B)  0.011 
C)  0.630 
D)  0.021

Question 17

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 18

Express y as a function of x. The constant C is a positive number.
-$3 \ln y = \frac { 1 } { 3 } \ln x - \ln \frac { x ^ { 2 } - 1 } { x ^ { 4 / 3 } } + \ln C$

Accepted Answer

A)  $y = \sqrt [ 3 ] { \frac { C } { x ^ { 1 / 3 } \left( x ^ { 2 } - 1 \right) } }$ 
B)  $y = \sqrt [ 3 ] { \frac { C x } { x ^ { 2 } - 1 } }$ 
C)  $y = \sqrt [ 3 ] { \frac { C x ^ { 1 / 3 } } { x ^ { 2 } - 1 } }$ 
D)  $y = \sqrt [ 3 ] { \frac { C x ^ { 5 / 3 } } { x ^ { 2 } - 1 } }$ 
A)  $y = \sqrt [ 3 ] { \frac { C } { x ^ { 1 / 3 } \left( x ^ { 2 } - 1 \right) } }$ 
B)  $y = \sqrt [ 3 ] { \frac { C x } { x ^ { 2 } - 1 } }$ 
C)  $y = \sqrt [ 3 ] { \frac { C x ^ { 1 / 3 } } { x ^ { 2 } - 1 } }$ 
D)  $y = \sqrt [ 3 ] { \frac { C x ^ { 5 / 3 } } { x ^ { 2 } - 1 } }$

Question 19

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }$$

Accepted Answer

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

Question 20

Solve the problem.
-Suppose that $f ( x ) = 2 ^ { x }$. What is $f ( 3 )$ ? What point is on the graph of $f$ ?

Accepted Answer

A)  $9 ; ( 2,9 )$ 
B)  $8 ; ( 3,2 )$ 
C)  $9 ; ( 3,9 )$ 
D)  $8 ; ( 3,8 )$ 
A)  $9 ; ( 2,9 )$ 
B)  $8 ; ( 3,2 )$ 
C)  $9 ; ( 3,9 )$ 
D)  $8 ; ( 3,8 )$

Indicate whether the function is one-to-one. -{(5, 4), (6, 4), (7, 3), (8, -9)}

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 5 } 5 ^ { 4.71 }$

Express as a single logarithm. - $3 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 2$

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. - $4 ^ { x + 7 } = 7$

Solve the problem. -The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $y = 270 ( 2.7 ) ^ { 0.07 t }$

Find the domain of the composite function f $f ^ { \circ } g$ - $\mathrm { f } ( \mathrm { x } ) = 7 \mathrm { x } + 14 ; \quad \mathrm { g } ( \mathrm { x } ) = \mathrm { x } + 7$

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

Solve the equation. - $8 + 5 \ln x = 16$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 4 } 4 ^ { - 15 }$

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

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

Express y as a function of x. The constant C is a positive number. - $3 \ln y = \frac { 1 } { 3 } \ln x - \ln \frac { x ^ { 2 } - 1 } { x ^ { 4 / 3 } } + \ln C$

Decide whether or not the functions are inverses of each other. - $f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }$

Solve the problem. -Suppose that $f ( x ) = 2 ^ { x }$ . What is $f ( 3 )$ ? What point is on the graph of $f$ ?

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

Review

Filters

Exam 4: Exponential and Logarithmic Functions

Indicate whether the function is one-to-one. -{(5, 4), (6, 4), (7, 3), (8, -9)}

The graph of a logarithmic function is shown. Select the function which matches the graph. - A) y=log⁡(x−3)y = \log ( x - 3 )y=log(x−3) B) y=log⁡(3−x)y = \log ( 3 - x )y=log(3−x) C) y=3−log⁡(x)y = 3 - \log ( x )y=3−log(x) D) y=log⁡(x)−3y = \log ( x ) - 3y=log(x)−3

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - log⁡554.71\log _ { 5 } 5 ^ { 4.71 }log5​54.71

Express as a single logarithm. - 3log⁡a(2x+1)−2log⁡a(2x−1)+23 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 23loga​(2x+1)−2loga​(2x−1)+2

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. - 4x+7=74 ^ { x + 7 } = 74x+7=7

Solve the problem. -The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use y=270(2.7)0.07ty = 270 ( 2.7 ) ^ { 0.07 t }y=270(2.7)0.07t

Find the domain of the composite function f f∘gf ^ { \circ } g f∘g - f(x)=7x+14;g(x)=x+7\mathrm { f } ( \mathrm { x } ) = 7 \mathrm { x } + 14 ; \quad \mathrm { g } ( \mathrm { x } ) = \mathrm { x } + 7f(x)=7x+14;g(x)=x+7

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

Solve the equation. - 8+5ln⁡x=168 + 5 \ln x = 168+5lnx=16

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - log⁡44−15\log _ { 4 } 4 ^ { - 15 }log4​4−15

The graph of a logarithmic function is shown. Select the function which matches the graph. - A) y=log⁡(x)y = \log ( x )y=log(x) B) y=log⁡(−x)y = \log ( - x )y=log(−x) C) y=−log⁡(−x)y = - \log ( - x )y=−log(−x) D) y=−log⁡(x)y = - \log ( x )y=−log(x)

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

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

Express y as a function of x. The constant C is a positive number. - 3ln⁡y=13ln⁡x−ln⁡x2−1x4/3+ln⁡C3 \ln y = \frac { 1 } { 3 } \ln x - \ln \frac { x ^ { 2 } - 1 } { x ^ { 4 / 3 } } + \ln C3lny=31​lnx−lnx4/3x2−1​+lnC

Decide whether or not the functions are inverses of each other. - f(x)=x3−8,g(x)=x+83f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }f(x)=x3−8,g(x)=3x+8​

Solve the problem. -Suppose that f(x)=2xf ( x ) = 2 ^ { x }f(x)=2x . What is f(3)f ( 3 )f(3) ? What point is on the graph of fff ?

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

Review

Filters

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 5 } 5 ^ { 4.71 }$

Express as a single logarithm. - $3 \log _ { a } ( 2 x + 1 ) - 2 \log _ { a } ( 2 x - 1 ) + 2$

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. - $4 ^ { x + 7 } = 7$

Solve the problem. -The rabbit population in a forest area grows at the rate of 7% monthly. If there are 270 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use $y = 270 ( 2.7 ) ^ { 0.07 t }$

Find the domain of the composite function f $f ^ { \circ } g$ - $\mathrm { f } ( \mathrm { x } ) = 7 \mathrm { x } + 14 ; \quad \mathrm { g } ( \mathrm { x } ) = \mathrm { x } + 7$

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

Solve the equation. - $8 + 5 \ln x = 16$

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $\log _ { 4 } 4 ^ { - 15 }$

Express y as a function of x. The constant C is a positive number. - $3 \ln y = \frac { 1 } { 3 } \ln x - \ln \frac { x ^ { 2 } - 1 } { x ^ { 4 / 3 } } + \ln C$

Decide whether or not the functions are inverses of each other. - $f ( x ) = x ^ { 3 } - 8 , g ( x ) = \sqrt [ 3 ] { x + 8 }$

Solve the problem. -Suppose that $f ( x ) = 2 ^ { x }$ . What is $f ( 3 )$ ? What point is on the graph of $f$ ?