Question 1

Find the domain of the composite function f $f ^ { \circ } g $
-$$f ( x ) = x + 8 ; \quad g ( x ) = \frac { 4 } { x + 6 }$$

Accepted Answer

A)  $\{ x \mid x \neq - 14 \}$ 
B)  $\{ x \mid x \neq - 6 \}$ 
C)  $\{ x \mid x \neq - 6 , x \neq - 8 \}$ 
D)  $\{ x \mid x$ is any real number $\}$ 
A)  $\{ x \mid x \neq - 14 \}$ 
B)  $\{ x \mid x \neq - 6 \}$ 
C)  $\{ x \mid x \neq - 6 , x \neq - 8 \}$ 
D)  $\{ x \mid x$ is any real number $\}$

Question 2

Solve the problem.
-Determine the domain of the function f(x) $f ( x ) = \log _ { 5 } ( x + 2 )$

Accepted Answer

The answer of Solve the problem.
-Determine the domain of the...

Question 3

Solve the problem.
-Gillian has $10,000 to invest in a mutual fund. The average annual rate of return for the past five years was
12.25%. Assuming this rate, determine how long it will take for her investment to double.

Accepted Answer

The answer of Solve the problem.
-Gillian has $10,000 to invest...

Question 4

Write as the sum and/or difference of logarithms. Express powers as factors.
-$\log _ { 12 } \sqrt { \frac { \mathrm { rs } } { 13 } }$

Accepted Answer

A)  $\frac { 1 } { 2 } \log _ { 12 } \mathrm { rs } - \frac { 1 } { 2 } \log _ { 12 } 13$ 
B)  $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } + \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} - \log _ { 12 } 13$ 
C)  $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } \cdot \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} \div \frac { 1 } { 2 } \log _ { 12 } 13$ 
D)  $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } + \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} - \frac { 1 } { 2 } \log _ { 12 } 13$ 
A)  $\frac { 1 } { 2 } \log _ { 12 } \mathrm { rs } - \frac { 1 } { 2 } \log _ { 12 } 13$ 
B)  $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } + \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} - \log _ { 12 } 13$ 
C)  $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } \cdot \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} \div \frac { 1 } { 2 } \log _ { 12 } 13$ 
D)  $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } + \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} - \frac { 1 } { 2 } \log _ { 12 } 13$

Question 5

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.
-$$f ( x ) = 4 ( x - 1 )$$
 
 A) domain of $f : ( - \infty , \infty )$; range of f: $( 0 , \infty )$
horizontal asymptote: $y = 0$

Accepted Answer

B)  domain of $f : ( - \infty , \infty )$; range of $f : ( 0 , \infty )$ 
horizontal asymptote: $\mathrm { y } = 0$ 
  
C) 
domain of $ \mathrm{f}:(-\infty, \infty) $; range of $ \mathrm{f}:(-\infty, 0) $ 
horizontal asymptote: $ y=0 $
  
D) 
domain of $ \mathrm{f}:(-\infty, \infty) $; range of $ \mathrm{f}:(-\infty, 0 $ horizontal asymptote: $ \mathrm{y}=0 $

Question 6

Find the exact value of the logarithmic expression.
-$\log _ { 4 } 16$

Accepted Answer

A)  2 
B)  8 
C)  16 
D)  4 
A)  2 
B)  8 
C)  16 
D)  4

Question 7

Solve the equation.
-$\log _ { 21 } ( x + 84 ) = 3 - \log _ { 21 } x$

Accepted Answer

A)  $\{ 63 \}$ 
B)  $\{ 147 \}$ 
C)  $\{ - 147 \}$ 
D)  $\{ - 63 \}$ 
A)  $\{ 63 \}$ 
B)  $\{ 147 \}$ 
C)  $\{ - 147 \}$ 
D)  $\{ - 63 \}$

Question 8

Find the domain of the composite function f $f ^ { \circ } g $
-$$f ( x ) = \frac { - 7 } { x } ; \quad g ( x ) = \frac { - 2 } { x + 1 }$$

Accepted Answer

A)  $\{ x \mid x \neq - 1 \}$ 
B)  $\{ x \mid x \neq - 1 , x \neq 0 \}$ 
C)  $\{ x \mid x$ is any real number $\}$ 
D)  $\{ x \mid x \neq 0 , x \neq - 1 , x \neq 7 \}$ 
A)  $\{ x \mid x \neq - 1 \}$ 
B)  $\{ x \mid x \neq - 1 , x \neq 0 \}$ 
C)  $\{ x \mid x$ is any real number $\}$ 
D)  $\{ x \mid x \neq 0 , x \neq - 1 , x \neq 7 \}$

Question 9

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 9 x - 9 , g ( x ) = \frac { 1 } { 9 } x + 1$$

Accepted Answer

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

Question 10

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this
function $$M ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) , \text { where } x _ { 0 } = 10 ^ { - 3 }$$
-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 11

Solve the equation.
-$$3^{ ( 9 - 4 x )} = 3$$

Accepted Answer

A)  $\{ 1 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ - 2 \}$ 
A)  $\{ 1 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ - 2 \}$

Question 12

Use a graphing calculator to solve the equation. Round your answer to two decimal places.
-$\log _ { 4 } x + \log _ { 3 } x = 3$

Accepted Answer

A)  {1.85} 
B)  {0.8} 
C)  {10.46} 
D)  {6.29} 
A)  {1.85} 
B)  {0.8} 
C)  {10.46} 
D)  {6.29}

Question 13

Find the effective rate of interest.
-$4 \frac { 3 } { 4 } \%$ compounded quarterly

Accepted Answer

The answer of Find the effective rate of interest.
-\(4 \frac...

Question 14

Find the inverse. Determine whether the inverse represents a function.
-$\{ ( 6,5 ) , ( - 1,6 ) , ( - 3,7 ) , ( - 5,8 ) \}$

Accepted Answer

A)  $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \} ;$ not a function 
B)  $\{ ( 4,3 ) , ( 3,8 ) , ( 6,10 ) , ( 4,5 ) \}$; not a function 
C)  $\{ ( 4,3 ) , ( 6,8 ) , ( 6,8 ) , ( 4,5 ) \} ;$ a function 
D)  $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \}$; a function 
A)  $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \} ;$ not a function 
B)  $\{ ( 4,3 ) , ( 3,8 ) , ( 6,10 ) , ( 4,5 ) \}$; not a function 
C)  $\{ ( 4,3 ) , ( 6,8 ) , ( 6,8 ) , ( 4,5 ) \} ;$ a function 
D)  $\{ ( 3,6 ) , ( 4,10 ) , ( 5,8 ) , ( 6,6 ) \}$; a function

Question 15

Solve the problem.
-Meike earned $1565 in tips while working a summer job at a coffee shop. She wants to use this money to take a
trip to Europe next summer. If she places the money in an account which pays 6.5% compounded continuously,
how much money will she have in nine months?

Accepted Answer

The answer of Solve the problem.
-Meike earned $1565 in tips...

Question 16

Solve the problem.
-A fossilized leaf contains 18% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.

Accepted Answer

A)  35,538 
B)  1,600 
C)  13,829 
D)  23,309 
A)  35,538 
B)  1,600 
C)  13,829 
D)  23,309

Question 17

Change the exponential expression to an equivalent expression involving a logarithm.
-$$\mathrm { e } ^ { \mathrm { x } } = 13$$

Accepted Answer

A)  $\log _ { 13 } x = e$ 
B)  $\ln 13 = x$ 
C)  $\log _ { \mathrm { X } } \mathrm { e } = 13$ 
D)  $\ln x = 13$ 
A)  $\log _ { 13 } x = e$ 
B)  $\ln 13 = x$ 
C)  $\log _ { \mathrm { X } } \mathrm { e } = 13$ 
D)  $\ln x = 13$

Question 18

Find the exact value of the logarithmic expression.
-$\ln 1$

Accepted Answer

A)  1 
B)  $\mathrm { e }$ 
C)  $- 1$ 
D)  0 
A)  1 
B)  $\mathrm { e }$ 
C)  $- 1$ 
D)  0

Question 19

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { \sqrt { 5 } } 215.3$

Accepted Answer

A)  6.68 
B)  3.34 
C)  0.15 
D)  0.35 
A)  6.68 
B)  3.34 
C)  0.15 
D)  0.35

Question 20

Solve the problem.
-Which of the two rates would yield the larger amount in 1 year: $9 \%$ compounded monthly or $9 \frac { 1 } { 4 } \%$ compounded annually?

Accepted Answer

A)  $9 \%$ compounded monthly 
B)  $9 \frac { 1 } { 4 } \%$ compounded annually 
C)  They will yield the same amount. 
A)  $9 \%$ compounded monthly 
B)  $9 \frac { 1 } { 4 } \%$ compounded annually 
C)  They will yield the same amount.

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = x + 8 ; \quad g ( x ) = \frac { 4 } { x + 6 }$

Solve the problem. -Determine the domain of the function f(x) $f ( x ) = \log _ { 5 } ( x + 2 )$

Solve the problem. -Gillian has $10,000 to invest in a mutual fund. The average annual rate of return for the past five years was 12.25%. Assuming this rate, determine how long it will take for her investment to double.

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 12 } \sqrt { \frac { \mathrm { rs } } { 13 } }$

Find the exact value of the logarithmic expression. - $\log _ { 4 } 16$

Solve the equation. - $\log _ { 21 } ( x + 84 ) = 3 - \log _ { 21 } x$

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \frac { - 7 } { x } ; \quad g ( x ) = \frac { - 2 } { x + 1 }$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 9 x - 9 , g ( x ) = \frac { 1 } { 9 } x + 1$

Solve the equation. - $3^{ ( 9 - 4 x )} = 3$

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\log _ { 4 } x + \log _ { 3 } x = 3$

Find the effective rate of interest. - $4 \frac { 3 } { 4 } \%$ compounded quarterly

Find the inverse. Determine whether the inverse represents a function. - $\{ ( 6,5 ) , ( - 1,6 ) , ( - 3,7 ) , ( - 5,8 ) \}$

Solve the problem. -Meike earned $1565 in tips while working a summer job at a coffee shop. She wants to use this money to take a trip to Europe next summer. If she places the money in an account which pays 6.5% compounded continuously, how much money will she have in nine months?

Solve the problem. -A fossilized leaf contains 18% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.

Change the exponential expression to an equivalent expression involving a logarithm. - $\mathrm { e } ^ { \mathrm { x } } = 13$

Find the exact value of the logarithmic expression. - $\ln 1$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { \sqrt { 5 } } 215.3$

Solve the problem. -Which of the two rates would yield the larger amount in 1 year: $9 \%$ compounded monthly or $9 \frac { 1 } { 4 } \%$ compounded annually?

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

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Exam 4: Exponential and Logarithmic Functions

Find the domain of the composite function f f∘gf ^ { \circ } g f∘g - f(x)=x+8;g(x)=4x+6f ( x ) = x + 8 ; \quad g ( x ) = \frac { 4 } { x + 6 }f(x)=x+8;g(x)=x+64​

Solve the problem. -Determine the domain of the function f(x) f(x)=log⁡5(x+2)f ( x ) = \log _ { 5 } ( x + 2 )f(x)=log5​(x+2)