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 $\}$

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)  $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } + \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} - \frac { 1 } { 2 } \log _ { 12 } 13$

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

Question 7

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

Accepted Answer

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)  $\{ x \mid x \neq 0 , x \neq - 1 , x \neq 7 \}$

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

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 answer of The Richter scale converts seismographic readings into...

Question 11

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

Accepted Answer

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}

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

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

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)  $\ln x = 13$

Question 18

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

Accepted Answer

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

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.

Exam 4: Exponential and Logarithmic Functions

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?

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)

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⁡12rs13\log _ { 12 } \sqrt { \frac { \mathrm { rs } } { 13 } }log12​13rs​​

Find the exact value of the logarithmic expression. - log⁡416\log _ { 4 } 16log4​16

Solve the equation. - log⁡21(x+84) =3−log⁡21x\log _ { 21 } ( x + 84 ) = 3 - \log _ { 21 } xlog21​(x+84) =3−log21​x

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

Decide whether or not the functions are inverses of each other. - f(x) =9x−9,g(x) =19x+1f ( x ) = 9 x - 9 , g ( x ) = \frac { 1 } { 9 } x + 1f(x) =9x−9,g(x) =91​x+1

Solve the equation. - 3(9−4x) =33^{ ( 9 - 4 x ) } = 33(9−4x) =3

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - log⁡4x+log⁡3x=3\log _ { 4 } x + \log _ { 3 } x = 3log4​x+log3​x=3

Find the effective rate of interest. - 434%4 \frac { 3 } { 4 } \%443​% compounded quarterly

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