Question 1

Determine whether the functions f and g are inverses of each other.
-$$f ( x ) = ( x + 4 ) ^ { 3 } + 1 ; g ( x ) = \sqrt [ 3 ] { x - 1 } - 4$$

Accepted Answer

A)  $Y e s$ 
B)  $\mathrm { No }$ 
A)  $Y e s$ 
B)  $\mathrm { No }$

Question 2

Graph the exponential function.
-$y=-5^{x}$

Accepted Answer

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

Question 3

Solve the equation for x. Give an exact solution.
-$\log 3 x = - 6$

Accepted Answer

A)  $\{ - 18 \}$ 
B)  $\left\{ \frac { 10 ^ { 3 } } { - 6 } \right\}$ 
C)  $\left\{ \frac { 10 ^ { - 6 } } { 3 } \right\}$ 
D)  $\{ - 20 \}$ 
A)  $\{ - 18 \}$ 
B)  $\left\{ \frac { 10 ^ { 3 } } { - 6 } \right\}$ 
C)  $\left\{ \frac { 10 ^ { - 6 } } { 3 } \right\}$ 
D)  $\{ - 20 \}$

Question 4

Use the power property to rewrite the expression.
-$\log _ { 6 } x ^ { 5 }$

Accepted Answer

A)  $6 \log _ { 5 } x$ 
B)  $5 \log _ { 6 } x ^ { 5 }$ 
C)  $5 \log _ { 6 } x$ 
D)  $6 \log x$ 
A)  $6 \log _ { 5 } x$ 
B)  $5 \log _ { 6 } x ^ { 5 }$ 
C)  $5 \log _ { 6 } x$ 
D)  $6 \log x$

Question 5

Solve the logarithmic equation. Give an exact solution.
-$\log _ { 4 } x = - 3$

Accepted Answer

A)  $\{ 64 \}$ 
B)  $\{ - 12 \}$ 
C)  $\left\{ \frac { 1 } { 16 } \right\}$ 
D)  $\left\{ \frac { 1 } { 64 } \right\}$ 
A)  $\{ 64 \}$ 
B)  $\{ - 12 \}$ 
C)  $\left\{ \frac { 1 } { 16 } \right\}$ 
D)  $\left\{ \frac { 1 } { 64 } \right\}$

Question 6

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$$\left( \log _ { a } x - \log _ { a } y \right) + 2 \log _ { a } z$$

Accepted Answer

A)  $\log _ { a } x z ^ { 2 } y$ 
B)  $\log _ { a } \frac { x } { z ^ { 2 } v }$ 
C)  $\log _ { a } \frac { 2 x z } { y }$ 
D)  $\log _ { a } \frac { x z ^ { 2 } } { y }$ 
A)  $\log _ { a } x z ^ { 2 } y$ 
B)  $\log _ { a } \frac { x } { z ^ { 2 } v }$ 
C)  $\log _ { a } \frac { 2 x z } { y }$ 
D)  $\log _ { a } \frac { x z ^ { 2 } } { y }$

Question 7

Solve the equation.
-$125 ^ { x - 2 } = 25$

Accepted Answer

A)  $\left\{ - \frac { 4 } { 3 } \right\}$ 
B)  $\{ 24 \}$ 
C)  $\left\{ \frac { 8 } { 3 } \right\}$ 
D)  $\{ 1 \}$ 
A)  $\left\{ - \frac { 4 } { 3 } \right\}$ 
B)  $\{ 24 \}$ 
C)  $\left\{ \frac { 8 } { 3 } \right\}$ 
D)  $\{ 1 \}$

Question 8

Write as an exponential equation.
-$$\log _ { \mathrm { e } } \mathrm { z } = 7$$

Accepted Answer

A)  $7 ^ { \mathrm { e } } = \mathrm { z }$ 
B)  $\mathrm { z } ^ { 7 } = \mathrm { e }$ 
C)  $e ^ { 7 } = z$ 
D)  $\mathrm { e } ^ { \mathrm { z } } = 7$ 
A)  $7 ^ { \mathrm { e } } = \mathrm { z }$ 
B)  $\mathrm { z } ^ { 7 } = \mathrm { e }$ 
C)  $e ^ { 7 } = z$ 
D)  $\mathrm { e } ^ { \mathrm { z } } = 7$

Question 9

Find the inverse of the one-to-one function.
-$$f ( x ) = \frac { 5 } { 6 x - 7 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 7 } { 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 } { 6 x } + \frac { 7 } { 6 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { 6 y } + \frac { 7 } { 6 }$ 
D)  $f ^ { - 1 } ( x ) = - \frac { 7 } { 6 } - \frac { 5 } { 6 x }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 7 } { 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { 5 } { 6 x } + \frac { 7 } { 6 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { 6 y } + \frac { 7 } { 6 }$ 
D)  $f ^ { - 1 } ( x ) = - \frac { 7 } { 6 } - \frac { 5 } { 6 x }$

Question 10

Solve the equation.
-$$4 ^ { - x } = \frac { 1 } { 16 }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 4 } \right\}$ 
B)  $\{ 2 \}$ 
C)  $\left\{ \frac { 1 } { 2 } \right\}$ 
D)  $\{ - 2 \}$ 
A)  $\left\{ \frac { 1 } { 4 } \right\}$ 
B)  $\{ 2 \}$ 
C)  $\left\{ \frac { 1 } { 2 } \right\}$ 
D)  $\{ - 2 \}$

Question 11

f(x)=8x - 7 ; g(x)=4x - 8 
Find  (f-g)(x) .

Accepted Answer

A)  $( f - g ) ( x ) = 4 x + 1$ 
B)  $( f - g ) ( x ) = 4 x - 15$ 
C)  $( f - g ) ( x ) = - 4 x - 1$ 
D)  $( f - g ) ( x ) = 12 x - 15$ 
A)  $( f - g ) ( x ) = 4 x + 1$ 
B)  $( f - g ) ( x ) = 4 x - 15$ 
C)  $( f - g ) ( x ) = - 4 x - 1$ 
D)  $( f - g ) ( x ) = 12 x - 15$

Question 12

Provide an appropriate response.
-If $f ( x ) = x , g ( x ) = x - 6$, and $h ( x ) = x ^ { 2 } - 5 x + 5$, find the composition $( g \circ h ) ( x )$

Accepted Answer

A)  $x ^ { 3 } - 11 x ^ { 2 } - 4 x - 30$ 
B)  $x ^ { 2 } - 5 x - 1$ 
C)  $x ^ { 2 } - 4 x - 1$ 
D)  $x ^ { 2 } - 17 x + 71$ 
A)  $x ^ { 3 } - 11 x ^ { 2 } - 4 x - 30$ 
B)  $x ^ { 2 } - 5 x - 1$ 
C)  $x ^ { 2 } - 4 x - 1$ 
D)  $x ^ { 2 } - 17 x + 71$

Question 13

Use a calculator to approximate the logarithm to four decimal places.
-$\log 123$

Accepted Answer

A)  $2.0934$ 
B)  $4.8122$ 
C)  $2.0864$ 
D)  $2.0899$ 
A)  $2.0934$ 
B)  $4.8122$ 
C)  $2.0864$ 
D)  $2.0899$

Question 14

$f ( x ) = \sqrt { 3 x } ; g ( x ) = - 2 x + 7$
Find $( f \cdot g ) ( x )$

Accepted Answer

A)  $( f \cdot g ) ( x ) = \sqrt { 3 x } + 14 x$ 
B)  $( f \cdot g ) ( x ) = - 2 x \sqrt { 3 x } + 7 \sqrt { 3 x }$ 
C)  $( f \cdot g ) ( x ) = - 6 x + 7 \sqrt { 3 x }$ 
D)  $( f \cdot g ) ( x ) = - 6 x ^ { 2 } + 21$ 
A)  $( f \cdot g ) ( x ) = \sqrt { 3 x } + 14 x$ 
B)  $( f \cdot g ) ( x ) = - 2 x \sqrt { 3 x } + 7 \sqrt { 3 x }$ 
C)  $( f \cdot g ) ( x ) = - 6 x + 7 \sqrt { 3 x }$ 
D)  $( f \cdot g ) ( x ) = - 6 x ^ { 2 } + 21$

Question 15

Solve for x.
-$$\log _ { 2 } x = - 3$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 9 } \right\}$ 
B)  $\{ - 1 \}$ 
C)  $\left\{ \frac { 1 } { 8 } \right\}$ 
D)  $\{ - 6 \}$ 
A)  $\left\{ \frac { 1 } { 9 } \right\}$ 
B)  $\{ - 1 \}$ 
C)  $\left\{ \frac { 1 } { 8 } \right\}$ 
D)  $\{ - 6 \}$

Question 16

Determine whether the function is a one-to-one function.
-$\begin{array}{l|c|c|c|c|c}
\text { Weekdays (input) } & \text { Monday } & \text { Tuesday } & \text { Wednesday } & \text { Thursday } & \text { Friday } \
\hline \text { Student: Avg. } & & & & & \
\text { Minutes of Study(outputt) } 249 & 324 & 410 & 123 & 144
\end{array}$

Accepted Answer

A)  one-to-one 
B)  not one-to-one 
A)  one-to-one 
B)  not one-to-one

Question 17

Graph the exponential function.
-$y=\left(\frac{1}{5}\right)^{x}+1$

Accepted Answer

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

Question 18

Solve for x.
-$$\log _ { 4 } 1 = x$$

Accepted Answer

A)  $\{ 1 \}$ 
B)  $\{ 16 \}$ 
C)  $\{ 0 \}$ 
D)  $\{ 4 \}$ 
A)  $\{ 1 \}$ 
B)  $\{ 16 \}$ 
C)  $\{ 0 \}$ 
D)  $\{ 4 \}$

Question 19

Graph the exponential function.
-$f(x)=2^{x+1}$

Accepted Answer

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

Question 20

Use the properties of logarithms to write the expression as a single logarithm.
-$$\log _ { 5 } x + 3 \log _ { 5 } x - \log _ { 5 } ( x + 6 )$$

Accepted Answer

A)  $\log _ { 5 } \left( \frac { x ^ { 2 } + 3 x } { x + 6 } \right)$ 
B)  $\log _ { 5 } \left( \frac { x ^ { 4 } } { x + 6 } \right)$ 
C)  $\log _ { 5 } \left( \frac { x ^ { 3 } } { x + 6 } \right)$ 
D)  $3 \log _ { 5 } \left( \frac { x ^ { 2 } } { x + 6 } \right)$ 
A)  $\log _ { 5 } \left( \frac { x ^ { 2 } + 3 x } { x + 6 } \right)$ 
B)  $\log _ { 5 } \left( \frac { x ^ { 4 } } { x + 6 } \right)$ 
C)  $\log _ { 5 } \left( \frac { x ^ { 3 } } { x + 6 } \right)$ 
D)  $3 \log _ { 5 } \left( \frac { x ^ { 2 } } { x + 6 } \right)$

Determine whether the functions f and g are inverses of each other. - $f ( x ) = ( x + 4 ) ^ { 3 } + 1 ; g ( x ) = \sqrt [ 3 ] { x - 1 } - 4$

Graph the exponential function. - $y=-5^{x}$ $Graph the exponential function. - y=-5^{x}$

Solve the equation for x. Give an exact solution. - $\log 3 x = - 6$

Use the power property to rewrite the expression. - $\log _ { 6 } x ^ { 5 }$

Solve the logarithmic equation. Give an exact solution. - $\log _ { 4 } x = - 3$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\left( \log _ { a } x - \log _ { a } y \right) + 2 \log _ { a } z$

Solve the equation. - $125 ^ { x - 2 } = 25$

Write as an exponential equation. - $\log _ { \mathrm { e } } \mathrm { z } = 7$

Find the inverse of the one-to-one function. - $f ( x ) = \frac { 5 } { 6 x - 7 }$

Solve the equation. - $4 ^ { - x } = \frac { 1 } { 16 }$

f(x)=8x - 7 ; g(x)=4x - 8 Find (f-g)(x) .

Provide an appropriate response. -If $f ( x ) = x , g ( x ) = x - 6$ , and $h ( x ) = x ^ { 2 } - 5 x + 5$ , find the composition $( g \circ h ) ( x )$

Use a calculator to approximate the logarithm to four decimal places. - $\log 123$

$f ( x ) = \sqrt { 3 x } ; g ( x ) = - 2 x + 7$ Find $( f \cdot g ) ( x )$

Solve for x. - $\log _ { 2 } x = - 3$

Determine whether the function is a one-to-one function. - Weekdays (input) Monday Tuesday Wednesday Thursday Friday Student: Avg. Minutes of Study(outputt) 249 324 410 123 144

Graph the exponential function. - $y=\left(\frac{1}{5}\right)^{x}+1$ $Graph the exponential function. - y=\left(\frac{1}{5}\right)^{x}+1$

Solve for x. - $\log _ { 4 } 1 = x$

Graph the exponential function. - $f(x)=2^{x+1}$ $Graph the exponential function. - f(x)=2^{x+1}$

Use the properties of logarithms to write the expression as a single logarithm. - $\log _ { 5 } x + 3 \log _ { 5 } x - \log _ { 5 } ( x + 6 )$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

Filters

Exam 9: Exponential and Logarithmic Functions

Determine whether the functions f and g are inverses of each other. - f(x)=(x+4)3+1;g(x)=x−13−4f ( x ) = ( x + 4 ) ^ { 3 } + 1 ; g ( x ) = \sqrt [ 3 ] { x - 1 } - 4f(x)=(x+4)3+1;g(x)=3x−1​−4

Graph the exponential function. - y=−5xy=-5^{x}y=−5x

Solve the equation for x. Give an exact solution. - log⁡3x=−6\log 3 x = - 6log3x=−6

Use the power property to rewrite the expression. - log⁡6x5\log _ { 6 } x ^ { 5 }log6​x5

Solve the logarithmic equation. Give an exact solution. - log⁡4x=−3\log _ { 4 } x = - 3log4​x=−3

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - (log⁡ax−log⁡ay)+2log⁡az\left( \log _ { a } x - \log _ { a } y \right) + 2 \log _ { a } z(loga​x−loga​y)+2loga​z

Solve the equation. - 125x−2=25125 ^ { x - 2 } = 25125x−2=25

Write as an exponential equation. - log⁡ez=7\log _ { \mathrm { e } } \mathrm { z } = 7loge​z=7

Find the inverse of the one-to-one function. - f(x)=56x−7f ( x ) = \frac { 5 } { 6 x - 7 }f(x)=6x−75​

Solve the equation. - 4−x=1164 ^ { - x } = \frac { 1 } { 16 }4−x=161​

f(x)=8x - 7 ; g(x)=4x - 8 Find (f-g)(x) .

Provide an appropriate response. -If f(x)=x,g(x)=x−6f ( x ) = x , g ( x ) = x - 6f(x)=x,g(x)=x−6 , and h(x)=x2−5x+5h ( x ) = x ^ { 2 } - 5 x + 5h(x)=x2−5x+5 , find the composition (g∘h)(x)( g \circ h ) ( x )(g∘h)(x)

Use a calculator to approximate the logarithm to four decimal places. - log⁡123\log 123log123

f(x)=3x;g(x)=−2x+7f ( x ) = \sqrt { 3 x } ; g ( x ) = - 2 x + 7f(x)=3x​;g(x)=−2x+7 Find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x)

Solve for x. - log⁡2x=−3\log _ { 2 } x = - 3log2​x=−3

Determine whether the function is a one-to-one function. - Weekdays (input) Monday Tuesday Wednesday Thursday Friday Student: Avg. Minutes of Study(outputt) 249 324 410 123 144

Graph the exponential function. - y=(15)x+1y=\left(\frac{1}{5}\right)^{x}+1y=(51​)x+1

Solve for x. - log⁡41=x\log _ { 4 } 1 = xlog4​1=x

Graph the exponential function. - f(x)=2x+1f(x)=2^{x+1}f(x)=2x+1

Use the properties of logarithms to write the expression as a single logarithm. - log⁡5x+3log⁡5x−log⁡5(x+6)\log _ { 5 } x + 3 \log _ { 5 } x - \log _ { 5 } ( x + 6 )log5​x+3log5​x−log5​(x+6)

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

Filters

Determine whether the functions f and g are inverses of each other. - $f ( x ) = ( x + 4 ) ^ { 3 } + 1 ; g ( x ) = \sqrt [ 3 ] { x - 1 } - 4$

Graph the exponential function. - $y=-5^{x}$ $Graph the exponential function. - y=-5^{x}$

Solve the equation for x. Give an exact solution. - $\log 3 x = - 6$

Use the power property to rewrite the expression. - $\log _ { 6 } x ^ { 5 }$

Solve the logarithmic equation. Give an exact solution. - $\log _ { 4 } x = - 3$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\left( \log _ { a } x - \log _ { a } y \right) + 2 \log _ { a } z$

Solve the equation. - $125 ^ { x - 2 } = 25$

Write as an exponential equation. - $\log _ { \mathrm { e } } \mathrm { z } = 7$

Find the inverse of the one-to-one function. - $f ( x ) = \frac { 5 } { 6 x - 7 }$

Solve the equation. - $4 ^ { - x } = \frac { 1 } { 16 }$

Provide an appropriate response. -If $f ( x ) = x , g ( x ) = x - 6$ , and $h ( x ) = x ^ { 2 } - 5 x + 5$ , find the composition $( g \circ h ) ( x )$

Use a calculator to approximate the logarithm to four decimal places. - $\log 123$

$f ( x ) = \sqrt { 3 x } ; g ( x ) = - 2 x + 7$ Find $( f \cdot g ) ( x )$

Solve for x. - $\log _ { 2 } x = - 3$

Graph the exponential function. - $y=\left(\frac{1}{5}\right)^{x}+1$ $Graph the exponential function. - y=\left(\frac{1}{5}\right)^{x}+1$

Solve for x. - $\log _ { 4 } 1 = x$

Graph the exponential function. - $f(x)=2^{x+1}$ $Graph the exponential function. - f(x)=2^{x+1}$

Use the properties of logarithms to write the expression as a single logarithm. - $\log _ { 5 } x + 3 \log _ { 5 } x - \log _ { 5 } ( x + 6 )$