Question 1

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$10,000 ^ { 4 x + 5 } = 10 ^ { 4 - x }$$

Accepted Answer

A)  $- \frac { 1 } { 17 }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $- \frac { 16 } { 17 }$ 
D)  $- \frac { 17 } { 16 }$ 
A)  $- \frac { 1 } { 17 }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $- \frac { 16 } { 17 }$ 
D)  $- \frac { 17 } { 16 }$

Question 2

a. Use transformations to graph the function.
b. Write the domain and range in interval notation.
c. Determine the vertical asymptote.
-$$y = 1 + \log _ { 5 } ( x )$$

Accepted Answer

A)  $\mathrm { a }$.

b. domain: $( 0 , \infty )$, range $( - \infty , \infty )$
c. vertical asymptote: $x = 0$ 
B)  $\mathrm { a }$.
 
b. domain: $( 1 , \infty )$, range $( - \infty , \infty )$
c. vertical asymptote: $x = 1$ 
C)  $\mathrm { a }$.
 
b. domain: $( 0 , \infty )$, range $( - \infty , \infty )$
c. vertical asymptote: $x = 0$ 
D)  $\mathrm { a }$.
 
b. domain: $( - 1 , \infty )$, range $( - \infty , \infty )$
c. vertical asymptote: $x = - 1$ 
A)  $\mathrm { a }$.

b. domain: $( 0 , \infty )$, range $( - \infty , \infty )$
c. vertical asymptote: $x = 0$ 
B)  $\mathrm { a }$.
 
b. domain: $( 1 , \infty )$, range $( - \infty , \infty )$
c. vertical asymptote: $x = 1$ 
C)  $\mathrm { a }$.
 
b. domain: $( 0 , \infty )$, range $( - \infty , \infty )$
c. vertical asymptote: $x = 0$ 
D)  $\mathrm { a }$.
 
b. domain: $( - 1 , \infty )$, range $( - \infty , \infty )$
c. vertical asymptote: $x = - 1$

Question 3

The graph of a function and its inverse are symmetric with respect to the line ______.

Accepted Answer

The answer of The graph of a function and its...

Question 4

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
-$\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } }$

Accepted Answer

A)  $\frac { 1 } { 4 } \log _ { 3 } x - 1$ 
B)  $\log _ { 3 } x - \log _ { 3 } 4 - 1$ 
C)  $\frac { 1 } { 4 } \log _ { 3 } x - \frac { 1 } { 4 }$ 
D)  $\log _ { 3 } \sqrt [ 4 ] { x } - \log _ { 3 } \sqrt [ 4 ] { 3 }$ 
A)  $\frac { 1 } { 4 } \log _ { 3 } x - 1$ 
B)  $\log _ { 3 } x - \log _ { 3 } 4 - 1$ 
C)  $\frac { 1 } { 4 } \log _ { 3 } x - \frac { 1 } { 4 }$ 
D)  $\log _ { 3 } \sqrt [ 4 ] { x } - \log _ { 3 } \sqrt [ 4 ] { 3 }$

Question 5

Given f (x), write an equation for $f ^ { - 1 } ( x )$ ) and then graph f (x) and $f ^ { - 1 } ( x )$ ) on the same coordinate system.
-$$f ( x ) = x ^ { 2 } - 9 ; x \leq 0$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x + 9 }$
  
B)  $f ^ { - 1 } ( x ) = - \sqrt { x + 9 }$
  
C)  $f ^ { - 1 } ( x ) = \sqrt { x + 9 }$
  
D)  $f ^ { - 1 } ( x ) = - \sqrt { x + 9 }$
  
A)  $f ^ { - 1 } ( x ) = \sqrt { x + 9 }$
  
B)  $f ^ { - 1 } ( x ) = - \sqrt { x + 9 }$
  
C)  $f ^ { - 1 } ( x ) = \sqrt { x + 9 }$
  
D)  $f ^ { - 1 } ( x ) = - \sqrt { x + 9 }$

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-$\log _{b} 1=\quad \text { because } b^{\square}=1$

Accepted Answer

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

Question 7

A one-to-one function is given. Write an expression for the inverse function.
-$$g ( x ) = r ( x + q ) ^ { 7 } + s$$

Accepted Answer

A)  $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { \frac { x } { r } - s - q }$ 
B)  $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { \frac { x } { r } - s } - q$ 
C)  $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { \frac { x - s } { r } } - q$ 
D)  $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { \frac { x - s } { r } - q }$ 
A)  $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { \frac { x } { r } - s - q }$ 
B)  $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { \frac { x } { r } - s } - q$ 
C)  $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { \frac { x - s } { r } } - q$ 
D)  $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { \frac { x - s } { r } - q }$

Question 8

Solve the problem.
-Based on data from a hurricane, the function defined by $w ( x ) = - 1.17 x + 1,225$ gives the wind speed $w ( x )$ (in mph) based on the barometric pressure $x$ (in millibars, mb). Write a function representing the inverse of $w$ and interpret its meaning in context.

Accepted Answer

A)  $w ^ { - 1 } ( x ) = \frac { 1,225 - x } { 1.17 }$ 
B)  $w ^ { - 1 } ( x ) = \frac { x - 1,225 } { 1.17 }$; The inverse gives the barometric pressure $w ^ { - 1 } ( x )$ for a given wind speed. 
C)  $w ^ { - 1 } ( x ) = \frac { 1,225 - x } { 1.17 }$; The inverse gives the barometric pressure $w ^ { - 1 } ( x )$ for a given wind speed. 
D)  $w ^ { - 1 } ( x ) = \frac { x - 1,225 } { 1.17 }$; The inverse gives the wind speed $w ^ { - 1 } ( x )$ for a given barometric pressure. 
A)  $w ^ { - 1 } ( x ) = \frac { 1,225 - x } { 1.17 }$ 
B)  $w ^ { - 1 } ( x ) = \frac { x - 1,225 } { 1.17 }$; The inverse gives the barometric pressure $w ^ { - 1 } ( x )$ for a given wind speed. 
C)  $w ^ { - 1 } ( x ) = \frac { 1,225 - x } { 1.17 }$; The inverse gives the barometric pressure $w ^ { - 1 } ( x )$ for a given wind speed. 
D)  $w ^ { - 1 } ( x ) = \frac { x - 1,225 } { 1.17 }$; The inverse gives the wind speed $w ^ { - 1 } ( x )$ for a given barometric pressure.

Question 9

Apply the power property of logarithms.
-$\ln 10 ^ { k t }$

Accepted Answer

A)  $10 \ln k t$ 
B)  $k t \ln 10$ 
C)  $k t + \ln 10$ 
D)  $10 \ln k \cdot 10 \ln t$ 
A)  $10 \ln k t$ 
B)  $k t \ln 10$ 
C)  $k t + \ln 10$ 
D)  $10 \ln k \cdot 10 \ln t$

Question 10

Solve the problem.
-$\$ 20,000$ is invested at $5.5 \%$ interest compounded monthly. How long will it take for the investment to double? Round to the nearest tenth of a year

Accepted Answer

A)  $12.6 \mathrm { yr }$ 
B)  $13.2 \mathrm { yr }$ 
C)  $10.7 \mathrm { yr }$ 
D)  $13.5 \mathrm { yr }$ 
A)  $12.6 \mathrm { yr }$ 
B)  $13.2 \mathrm { yr }$ 
C)  $10.7 \mathrm { yr }$ 
D)  $13.5 \mathrm { yr }$

Question 11

Solve the equation. Write the solution set with the exact solutions.
-$\ln x + \ln ( x - 4 ) = \ln ( 5 x - 14 )$

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\{ 7 \}$ 
C)  $\{ 2,7 \}$ 
D) {  } 
A)  $\{ 2 \}$ 
B)  $\{ 7 \}$ 
C)  $\{ 2,7 \}$ 
D) {  }

Question 12

A function f is a ________ -________ - ________function if for a and b in the domain of f, if $a \neq b , \text { then } f ( a ) \neq f ( b )$

Accepted Answer

The answer of A function f is a ________ -________...

Question 13

Write as the sum or difference of logarithms and fully simplify, if possible. Assume the variable
represents a positive real number.
-$\log \left( \frac { 1,000 } { \sqrt { x ^ { 2 } + 25 } } \right)$

Accepted Answer

A)  $3 - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 25 \right)$ 
B)  $3 + \frac { 1 } { 2 } \log \left( x ^ { 2 } + 25 \right)$ 
C)  $3 - \log \left( \sqrt { x ^ { 2 } + 25 } \right)$ 
D)  $3 - \log ( x + 5 )$ 
A)  $3 - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 25 \right)$ 
B)  $3 + \frac { 1 } { 2 } \log \left( x ^ { 2 } + 25 \right)$ 
C)  $3 - \log \left( \sqrt { x ^ { 2 } + 25 } \right)$ 
D)  $3 - \log ( x + 5 )$

Question 14

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as
possible.
-$\ln p + \ln 2$

Accepted Answer

A)  $\ln 2 + p$ 
B)  $\ln 2 p$ 
C)  $\ln p ^ { 2 }$ 
D)  $\ln \frac { 2 } { p }$ 
A)  $\ln 2 + p$ 
B)  $\ln 2 p$ 
C)  $\ln p ^ { 2 }$ 
D)  $\ln \frac { 2 } { p }$

Question 15

Solve the equation. Write the solution set with the exact values given in terms of natural or common
logarithms. Also give approximate solutions to 4 decimal places, if necessary.
-$e ^ { 2 x } - 3 e ^ { x } - 10 = 0$; use natural logarithms

Accepted Answer

A)  $\{ \ln 5 \} ; x \approx 1.6094$ 
B)  $\{ \ln 5 , - \ln 2 \} ; x \approx 1.6094$ or $- 0.6931$ 
C)  $\{ \ln 5 , \ln ( - 2 ) \} ; x \approx 1.6094$ or $- 0.6931$ 
D)  \{ \} 
A)  $\{ \ln 5 \} ; x \approx 1.6094$ 
B)  $\{ \ln 5 , - \ln 2 \} ; x \approx 1.6094$ or $- 0.6931$ 
C)  $\{ \ln 5 , \ln ( - 2 ) \} ; x \approx 1.6094$ or $- 0.6931$ 
D)  \{ \}

Question 16

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
-$\log _ { 6 } \left( \frac { x ^ { 2 } } { y z } \right)$

Accepted Answer

A)  $\log _ { 6 } 2 x + \log _ { 6 } y + \log _ { 6 } z$ 
B)  $\log _ { 6 } 2 x - \log _ { 6 } y - \log _ { 6 } z$ 
C)  $2 \log _ { 6 } x + \log _ { 6 } y + \log _ { 6 } z$ 
D)  $2 \log _ { 6 } x - \log _ { 6 } y - \log _ { 6 } z$ 
A)  $\log _ { 6 } 2 x + \log _ { 6 } y + \log _ { 6 } z$ 
B)  $\log _ { 6 } 2 x - \log _ { 6 } y - \log _ { 6 } z$ 
C)  $2 \log _ { 6 } x + \log _ { 6 } y + \log _ { 6 } z$ 
D)  $2 \log _ { 6 } x - \log _ { 6 } y - \log _ { 6 } z$

Question 17

Approximate the value of the logarithm to four decimal places.
-$\log 38,018,195$

Accepted Answer

A)  3.8018 
B)  17.4536 
C)  7.5800 
D)  10.8018 
A)  3.8018 
B)  17.4536 
C)  7.5800 
D)  10.8018

Question 18

Graph the function and write the domain and range in interval notation.
-$$f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$$

Accepted Answer

A) 
 
Domain: $ (0, \infty) $
Range: $ (-\infty, \infty) $ 
B)

Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$ 
C) 
 
Domain: $( 0 , \infty )$
Range: $( - \infty , \infty )$ 
D) 
 
Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$ 
A) 
 
Domain: $ (0, \infty) $
Range: $ (-\infty, \infty) $ 
B)

Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$ 
C) 
 
Domain: $( 0 , \infty )$
Range: $( - \infty , \infty )$ 
D) 
 
Domain: $( - \infty , \infty )$
Range: $( 0 , \infty )$

Question 19

Graph the function.
-$$y = \log _ { 7 } x$$

Accepted Answer

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

Question 20

Solve the equation. Write the solution set with the exact values given in terms of natural or common
logarithms. Also give approximate solutions to 4 decimal places, if necessary.
-$1,462 = 18 ^ { x } + 7$; use natural logarithms

Accepted Answer

A)  $\left\{ \frac { \ln 1,455 } { \ln 18 } \right\} ; x \approx 2.5197$ 
B)  $\left\{ \frac { \ln 1,469 } { \ln 18 } \right\} ; x \approx 2.5230$ 
C)  $\left\{ \frac { \ln 1,469 } { 18 } \right\} ; x \approx 0.4051$ 
D)  \{ \} 
A)  $\left\{ \frac { \ln 1,455 } { \ln 18 } \right\} ; x \approx 2.5197$ 
B)  $\left\{ \frac { \ln 1,469 } { \ln 18 } \right\} ; x \approx 2.5230$ 
C)  $\left\{ \frac { \ln 1,469 } { 18 } \right\} ; x \approx 0.4051$ 
D)  \{ \}

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $10,000 ^ { 4 x + 5 } = 10 ^ { 4 - x }$

a. Use transformations to graph the function. b. Write the domain and range in interval notation. c. Determine the vertical asymptote. - $y = 1 + \log _ { 5 } ( x )$

The graph of a function and its inverse are symmetric with respect to the line ______.

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } }$

Given f (x), write an equation for $f ^ { - 1 } ( x )$ ) and then graph f (x) and $f ^ { - 1 } ( x )$ ) on the same coordinate system. - $f ( x ) = x ^ { 2 } - 9 ; x \leq 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $\log _{b} 1=\quad \text { because } b^{\square}=1$

A one-to-one function is given. Write an expression for the inverse function. - $g ( x ) = r ( x + q ) ^ { 7 } + s$

Solve the problem. -Based on data from a hurricane, the function defined by $w ( x ) = - 1.17 x + 1,225$ gives the wind speed $w ( x )$ (in mph) based on the barometric pressure $x$ (in millibars, mb). Write a function representing the inverse of $w$ and interpret its meaning in context.

Apply the power property of logarithms. - $\ln 10 ^ { k t }$

Solve the problem. - $\$ 20,000$ is invested at $5.5 \%$ interest compounded monthly. How long will it take for the investment to double? Round to the nearest tenth of a year

Solve the equation. Write the solution set with the exact solutions. - $\ln x + \ln ( x - 4 ) = \ln ( 5 x - 14 )$

A function f is a - - function if for a and b in the domain of f, if $a \neq b , \text { then } f ( a ) \neq f ( b )$

Write as the sum or difference of logarithms and fully simplify, if possible. Assume the variable represents a positive real number. - $\log \left( \frac { 1,000 } { \sqrt { x ^ { 2 } + 25 } } \right)$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\ln p + \ln 2$

Solve the equation. Write the solution set with the exact values given in terms of natural or common logarithms. Also give approximate solutions to 4 decimal places, if necessary. - $e ^ { 2 x } - 3 e ^ { x } - 10 = 0$ ; use natural logarithms

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 6 } \left( \frac { x ^ { 2 } } { y z } \right)$

Approximate the value of the logarithm to four decimal places. - $\log 38,018,195$

Graph the function and write the domain and range in interval notation. - $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$

Graph the function. - $y = \log _ { 7 } x$

Solve the equation. Write the solution set with the exact values given in terms of natural or common logarithms. Also give approximate solutions to 4 decimal places, if necessary. - $1,462 = 18 ^ { x } + 7$ ; use natural logarithms

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

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Exam 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 10,0004x+5=104−x10,000 ^ { 4 x + 5 } = 10 ^ { 4 - x }10,0004x+5=104−x

a. Use transformations to graph the function. b. Write the domain and range in interval notation. c. Determine the vertical asymptote. - y=1+log⁡5(x)y = 1 + \log _ { 5 } ( x )y=1+log5​(x)

The graph of a function and its inverse are symmetric with respect to the line ______.

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - log⁡3x34\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } }log3​43x​​

Given f (x), write an equation for f−1(x)f ^ { - 1 } ( x )f−1(x) ) and then graph f (x) and f−1(x)f ^ { - 1 } ( x )f−1(x) ) on the same coordinate system. - f(x)=x2−9;x≤0f ( x ) = x ^ { 2 } - 9 ; x \leq 0f(x)=x2−9;x≤0

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - log⁡b1= because b□=1\log _{b} 1=\quad \text { because } b^{\square}=1logb​1= because b□=1

A one-to-one function is given. Write an expression for the inverse function. - g(x)=r(x+q)7+sg ( x ) = r ( x + q ) ^ { 7 } + sg(x)=r(x+q)7+s

Apply the power property of logarithms. - ln⁡10kt\ln 10 ^ { k t }ln10kt

Solve the problem. - $20,000\$ 20,000$20,000 is invested at 5.5%5.5 \%5.5% interest compounded monthly. How long will it take for the investment to double? Round to the nearest tenth of a year

Solve the equation. Write the solution set with the exact solutions. - ln⁡x+ln⁡(x−4)=ln⁡(5x−14)\ln x + \ln ( x - 4 ) = \ln ( 5 x - 14 )lnx+ln(x−4)=ln(5x−14)

A function f is a ________ -________ - ________function if for a and b in the domain of f, if a≠b, then f(a)≠f(b)a \neq b , \text { then } f ( a ) \neq f ( b )a=b, then f(a)=f(b)

Write as the sum or difference of logarithms and fully simplify, if possible. Assume the variable represents a positive real number. - log⁡(1,000x2+25)\log \left( \frac { 1,000 } { \sqrt { x ^ { 2 } + 25 } } \right)log(x2+25​1,000​)

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - ln⁡p+ln⁡2\ln p + \ln 2lnp+ln2

Solve the equation. Write the solution set with the exact values given in terms of natural or common logarithms. Also give approximate solutions to 4 decimal places, if necessary. - e2x−3ex−10=0e ^ { 2 x } - 3 e ^ { x } - 10 = 0e2x−3ex−10=0 ; use natural logarithms

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - log⁡6(x2yz)\log _ { 6 } \left( \frac { x ^ { 2 } } { y z } \right)log6​(yzx2​)

Approximate the value of the logarithm to four decimal places. - log⁡38,018,195\log 38,018,195log38,018,195

Graph the function and write the domain and range in interval notation. - f(x)=(12)xf ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }f(x)=(21​)x

Graph the function. - y=log⁡7xy = \log _ { 7 } xy=log7​x

Solve the equation. Write the solution set with the exact values given in terms of natural or common logarithms. Also give approximate solutions to 4 decimal places, if necessary. - 1,462=18x+71,462 = 18 ^ { x } + 71,462=18x+7 ; use natural logarithms

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $10,000 ^ { 4 x + 5 } = 10 ^ { 4 - x }$

a. Use transformations to graph the function. b. Write the domain and range in interval notation. c. Determine the vertical asymptote. - $y = 1 + \log _ { 5 } ( x )$

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } }$

Given f (x), write an equation for $f ^ { - 1 } ( x )$ ) and then graph f (x) and $f ^ { - 1 } ( x )$ ) on the same coordinate system. - $f ( x ) = x ^ { 2 } - 9 ; x \leq 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $\log _{b} 1=\quad \text { because } b^{\square}=1$

A one-to-one function is given. Write an expression for the inverse function. - $g ( x ) = r ( x + q ) ^ { 7 } + s$

Apply the power property of logarithms. - $\ln 10 ^ { k t }$

Solve the problem. - $\$ 20,000$ is invested at $5.5 \%$ interest compounded monthly. How long will it take for the investment to double? Round to the nearest tenth of a year

Solve the equation. Write the solution set with the exact solutions. - $\ln x + \ln ( x - 4 ) = \ln ( 5 x - 14 )$

A function f is a - - function if for a and b in the domain of f, if $a \neq b , \text { then } f ( a ) \neq f ( b )$

Write as the sum or difference of logarithms and fully simplify, if possible. Assume the variable represents a positive real number. - $\log \left( \frac { 1,000 } { \sqrt { x ^ { 2 } + 25 } } \right)$

Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible. - $\ln p + \ln 2$

Solve the equation. Write the solution set with the exact values given in terms of natural or common logarithms. Also give approximate solutions to 4 decimal places, if necessary. - $e ^ { 2 x } - 3 e ^ { x } - 10 = 0$ ; use natural logarithms

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. - $\log _ { 6 } \left( \frac { x ^ { 2 } } { y z } \right)$

Approximate the value of the logarithm to four decimal places. - $\log 38,018,195$

Graph the function and write the domain and range in interval notation. - $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$

Graph the function. - $y = \log _ { 7 } x$

Solve the equation. Write the solution set with the exact values given in terms of natural or common logarithms. Also give approximate solutions to 4 decimal places, if necessary. - $1,462 = 18 ^ { x } + 7$ ; use natural logarithms