Question 1

$f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 3 x - 6$
Find $( f - g ) ( x )$

Accepted Answer

A)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 3 x + 6$ 
B)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 3 x - 6$ 
C)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } + 3 x + 6$ 
D)  $( f - g ) ( x ) = - \sqrt [ 3 ] { x } - 3 x + 6$ 
A)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 3 x + 6$ 
B)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } - 3 x - 6$ 
C)  $( f - g ) ( x ) = \sqrt [ 3 ] { x } + 3 x + 6$ 
D)  $( f - g ) ( x ) = - \sqrt [ 3 ] { x } - 3 x + 6$ A

Question 2

Graph the inverse of the function on the same set of axes.
-

Accepted Answer

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

Question 3

Graph the inverse of the function on the same set of axes.
-

Accepted Answer

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

Question 4

Graph the function and its inverse on the same set of axes.
-$$f ( x ) = \frac { 1 } { 2 } x - 2$$

Accepted Answer

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

Question 5

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$$\log _ { b } c - \log _ { b } d$$

Accepted Answer

A)  $\log _ { b } ( c - d )$ 
B)  $\log _ { b } \frac { d } { c }$ 
C)  $\log _ { 2 b } \frac { c } { d }$ 
D)  $\log _ { b } \frac { c } { d }$ 
A)  $\log _ { b } ( c - d )$ 
B)  $\log _ { b } \frac { d } { c }$ 
C)  $\log _ { 2 b } \frac { c } { d }$ 
D)  $\log _ { b } \frac { c } { d }$

Question 6

Solve the equation. Give an approximate solution to four decimal places.
-$5 ^ { x + 6 } = 5$

Accepted Answer

A)  $\{ - 5.0000 \}$ 
B)  $\{ 1.7782 \}$ 
C)  $\{ - 0.7782 \}$ 
D)  $\{ 7.0000 \}$ 
A)  $\{ - 5.0000 \}$ 
B)  $\{ 1.7782 \}$ 
C)  $\{ - 0.7782 \}$ 
D)  $\{ 7.0000 \}$

Question 7

For the given functions f and g, find the composition.
-$$f ( x ) = x ^ { 3 } + 6 x ; g ( x ) = - 3 x$$
Find $( f \circ g ) ( x )$.

Accepted Answer

A)  $- 27 x ^ { 3 } - 18 x$ 
B)  $- 27 x ^ { 2 } - 18 x$ 
C)  $- 3 x ^ { 3 } + 6 x$ 
D)  $- 3 x ^ { 3 } - 18 x$ 
A)  $- 27 x ^ { 3 } - 18 x$ 
B)  $- 27 x ^ { 2 } - 18 x$ 
C)  $- 3 x ^ { 3 } + 6 x$ 
D)  $- 3 x ^ { 3 } - 18 x$

Question 8

Use a calculator to approximate the logarithm to four decimal places.
-$\log 0.0748$

Accepted Answer

A)  $- 1.1261$ 
B)  $- 1.1319$ 
C)  $- 2.5929$ 
D)  $- 1.1203$ 
A)  $- 1.1261$ 
B)  $- 1.1319$ 
C)  $- 2.5929$ 
D)  $- 1.1203$

Question 9

Write the expression as sums or differences of multiples of logarithms.
-$\log _ { y } \frac { 11 x } { 2 }$

Accepted Answer

A)  $\log _ { y } 11 + \log _ { y } x + \log _ { y } 2$ 
B)  $\log _ { y } 11 x - \log _ { y } 2$ 
C)  $\log _ { y } 9 x$ 
D)  $\log _ { y } 11 + \log _ { y } x - \log _ { y } 2$ 
A)  $\log _ { y } 11 + \log _ { y } x + \log _ { y } 2$ 
B)  $\log _ { y } 11 x - \log _ { y } 2$ 
C)  $\log _ { y } 9 x$ 
D)  $\log _ { y } 11 + \log _ { y } x - \log _ { y } 2$

Question 10

Graph the function.
-$f ( x ) = 3 \log x$

Accepted Answer

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

Question 11

Determine whether the functions f and g are inverses of each other.
-$$f ( x ) = 3 x + 2 ; g ( x ) = \frac { x + 2 } { 3 }$$

Accepted Answer

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

Question 12

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-$$f = \{ ( 6 , - 2 ) , ( 9 , - 1 ) , ( 7,0 ) , ( 5,1 ) \}$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } = \{ ( - 1 , - 2 ) , ( - 2,7 ) , ( 6,9 ) , ( - 1,0 ) \}$ 
B)  $\mathrm { f } ^ { - 1 } = \{ ( - 1 , - 2 ) , ( 1,7 ) , ( 6,7 ) , ( - 1,0 ) \}$ 
C)  $\mathrm { f } ^ { - 1 } = \{ ( - 2,6 ) , ( - 1,9 ) , ( 0,7 ) , ( 1,5 ) \}$ 
D)  not one-to-one 
A)  $\mathrm { f } ^ { - 1 } = \{ ( - 1 , - 2 ) , ( - 2,7 ) , ( 6,9 ) , ( - 1,0 ) \}$ 
B)  $\mathrm { f } ^ { - 1 } = \{ ( - 1 , - 2 ) , ( 1,7 ) , ( 6,7 ) , ( - 1,0 ) \}$ 
C)  $\mathrm { f } ^ { - 1 } = \{ ( - 2,6 ) , ( - 1,9 ) , ( 0,7 ) , ( 1,5 ) \}$ 
D)  not one-to-one

Question 13

For the given functions f and g, find the composition.
-$$f ( x ) = \sqrt { x + 3 } ; g ( x ) = 8 x - 7$$
Find $( f \circ g ) ( x )$.

Accepted Answer

A)  $8 \sqrt { x - 4 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x + 3 } - 7$ 
A)  $8 \sqrt { x - 4 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x + 3 } - 7$

Question 14

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$$\log _ { 5 } 7 + \log _ { 5 } x$$

Accepted Answer

A)  $\log _ { 35 } x$ 
B)  $\log _ { 5 } 7 x$ 
C)  $\log _ { 5 } ( x + 7 )$ 
D)  $\log _ { 5 } 7 ^ { x }$ 
A)  $\log _ { 35 } x$ 
B)  $\log _ { 5 } 7 x$ 
C)  $\log _ { 5 } ( x + 7 )$ 
D)  $\log _ { 5 } 7 ^ { x }$

Question 15

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$$\log _ { 7 } 9 - \log _ { 7 } 6$$

Accepted Answer

A)  $\log _ { 7 } \frac { 2 } { 3 }$ 
B)  $\log _ { 7 } 3$ 
C)  $\log _ { 7 } \frac { 3 } { 2 }$ 
D)  $\log _ { 14 } \frac { 3 } { 2 }$ 
A)  $\log _ { 7 } \frac { 2 } { 3 }$ 
B)  $\log _ { 7 } 3$ 
C)  $\log _ { 7 } \frac { 3 } { 2 }$ 
D)  $\log _ { 14 } \frac { 3 } { 2 }$

Question 16

Solve the equation for x. Give an approximate solution accurate to four decimal places.
-$\ln ( 13 x + 3 ) = - 1.9$

Accepted Answer

A)  $\{ - 0.9501 \}$ 
B)  $\{ - 2.8504 \}$ 
C)  $\{ - 0.2193 \}$ 
D)  $\{ - 37.0552 \}$ 
A)  $\{ - 0.9501 \}$ 
B)  $\{ - 2.8504 \}$ 
C)  $\{ - 0.2193 \}$ 
D)  $\{ - 37.0552 \}$

Question 17

Find the inverse of the one-to-one function.
-$$f ( x ) = 5 x + 7$$

Accepted Answer

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

Question 18

Find the exact value.
-$\log \sqrt { 10 }$

Accepted Answer

A)  2 
B)  $- 2$ 
C)  5 
D)  $\frac { 1 } { 2 }$ 
A)  2 
B)  $- 2$ 
C)  5 
D)  $\frac { 1 } { 2 }$

Question 19

Solve the equation.
-$$3 ( 6 + 3 x ) = \frac { 1 } { 27 }$$

Accepted Answer

A)  $\{ 9 \}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$ 
A)  $\{ 9 \}$ 
B)  $\left\{ \frac { 1 } { 9 } \right\}$ 
C)  $\{ 3 \}$ 
D)  $\{ - 3 \}$

Question 20

Solve the equation. Give an exact solution.
-$$8 ^ { x } = 13$$

Accepted Answer

A)  $\{ \log 13 \log 8 \}$ 
B)  $\left\{ \frac { \log 8 } { \log 13 } \right\}$ 
C)  $\left\{ \frac { 13 } { 8 } \right\}$ 
D)  $\left\{ \frac { \log 13 } { \log 8 } \right\}$ 
A)  $\{ \log 13 \log 8 \}$ 
B)  $\left\{ \frac { \log 8 } { \log 13 } \right\}$ 
C)  $\left\{ \frac { 13 } { 8 } \right\}$ 
D)  $\left\{ \frac { \log 13 } { \log 8 } \right\}$

$f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 3 x - 6$ Find $( f - g ) ( x )$

Graph the inverse of the function on the same set of axes. -

Graph the inverse of the function on the same set of axes. -

Graph the function and its inverse on the same set of axes. - $f ( x ) = \frac { 1 } { 2 } x - 2$ $Graph the function and its inverse on the same set of axes. - f ( x ) = \frac { 1 } { 2 } x - 2$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { b } c - \log _ { b } d$

Solve the equation. Give an approximate solution to four decimal places. - $5 ^ { x + 6 } = 5$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 3 } + 6 x ; g ( x ) = - 3 x$ Find $( f \circ g ) ( x )$ .

Use a calculator to approximate the logarithm to four decimal places. - $\log 0.0748$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { y } \frac { 11 x } { 2 }$

Graph the function. - $f ( x ) = 3 \log x$ $Graph the function. - f ( x ) = 3 \log x$

Determine whether the functions f and g are inverses of each other. - $f ( x ) = 3 x + 2 ; g ( x ) = \frac { x + 2 } { 3 }$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $f = \{ ( 6 , - 2 ) , ( 9 , - 1 ) , ( 7,0 ) , ( 5,1 ) \}$

For the given functions f and g, find the composition. - $f ( x ) = \sqrt { x + 3 } ; g ( x ) = 8 x - 7$ Find $( f \circ g ) ( x )$ .

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 5 } 7 + \log _ { 5 } x$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 7 } 9 - \log _ { 7 } 6$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\ln ( 13 x + 3 ) = - 1.9$

Find the inverse of the one-to-one function. - $f ( x ) = 5 x + 7$

Find the exact value. - $\log \sqrt { 10 }$

Solve the equation. - $3 ( 6 + 3 x ) = \frac { 1 } { 27 }$

Solve the equation. Give an exact solution. - $8 ^ { x } = 13$

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

f(x)=x3;g(x)=3x−6f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 3 x - 6f(x)=3x​;g(x)=3x−6 Find (f−g)(x)( f - g ) ( x )(f−g)(x)

Graph the inverse of the function on the same set of axes. -

Graph the inverse of the function on the same set of axes. -

Graph the function and its inverse on the same set of axes. - f(x)=12x−2f ( x ) = \frac { 1 } { 2 } x - 2f(x)=21​x−2

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡bc−log⁡bd\log _ { b } c - \log _ { b } dlogb​c−logb​d

Solve the equation. Give an approximate solution to four decimal places. - 5x+6=55 ^ { x + 6 } = 55x+6=5

For the given functions f and g, find the composition. - f(x)=x3+6x;g(x)=−3xf ( x ) = x ^ { 3 } + 6 x ; g ( x ) = - 3 xf(x)=x3+6x;g(x)=−3x Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) .

Use a calculator to approximate the logarithm to four decimal places. - log⁡0.0748\log 0.0748log0.0748

Write the expression as sums or differences of multiples of logarithms. - log⁡y11x2\log _ { y } \frac { 11 x } { 2 }logy​211x​

Graph the function. - f(x)=3log⁡xf ( x ) = 3 \log xf(x)=3logx

Determine whether the functions f and g are inverses of each other. - f(x)=3x+2;g(x)=x+23f ( x ) = 3 x + 2 ; g ( x ) = \frac { x + 2 } { 3 }f(x)=3x+2;g(x)=3x+2​

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - f={(6,−2),(9,−1),(7,0),(5,1)}f = \{ ( 6 , - 2 ) , ( 9 , - 1 ) , ( 7,0 ) , ( 5,1 ) \}f={(6,−2),(9,−1),(7,0),(5,1)}

For the given functions f and g, find the composition. - f(x)=x+3;g(x)=8x−7f ( x ) = \sqrt { x + 3 } ; g ( x ) = 8 x - 7f(x)=x+3​;g(x)=8x−7 Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) .

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡57+log⁡5x\log _ { 5 } 7 + \log _ { 5 } xlog5​7+log5​x

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡79−log⁡76\log _ { 7 } 9 - \log _ { 7 } 6log7​9−log7​6

Solve the equation for x. Give an approximate solution accurate to four decimal places. - ln⁡(13x+3)=−1.9\ln ( 13 x + 3 ) = - 1.9ln(13x+3)=−1.9

Find the inverse of the one-to-one function. - f(x)=5x+7f ( x ) = 5 x + 7f(x)=5x+7

Find the exact value. - log⁡10\log \sqrt { 10 }log10​

Solve the equation. - 3(6+3x)=1273 ( 6 + 3 x ) = \frac { 1 } { 27 }3(6+3x)=271​

Solve the equation. Give an exact solution. - 8x=138 ^ { x } = 138x=13

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

$f ( x ) = \sqrt [ 3 ] { x } ; g ( x ) = 3 x - 6$ Find $( f - g ) ( x )$

Graph the function and its inverse on the same set of axes. - $f ( x ) = \frac { 1 } { 2 } x - 2$ $Graph the function and its inverse on the same set of axes. - f ( x ) = \frac { 1 } { 2 } x - 2$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { b } c - \log _ { b } d$

Solve the equation. Give an approximate solution to four decimal places. - $5 ^ { x + 6 } = 5$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 3 } + 6 x ; g ( x ) = - 3 x$ Find $( f \circ g ) ( x )$ .

Use a calculator to approximate the logarithm to four decimal places. - $\log 0.0748$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { y } \frac { 11 x } { 2 }$

Graph the function. - $f ( x ) = 3 \log x$ $Graph the function. - f ( x ) = 3 \log x$

Determine whether the functions f and g are inverses of each other. - $f ( x ) = 3 x + 2 ; g ( x ) = \frac { x + 2 } { 3 }$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $f = \{ ( 6 , - 2 ) , ( 9 , - 1 ) , ( 7,0 ) , ( 5,1 ) \}$

For the given functions f and g, find the composition. - $f ( x ) = \sqrt { x + 3 } ; g ( x ) = 8 x - 7$ Find $( f \circ g ) ( x )$ .

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 5 } 7 + \log _ { 5 } x$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 7 } 9 - \log _ { 7 } 6$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\ln ( 13 x + 3 ) = - 1.9$

Find the inverse of the one-to-one function. - $f ( x ) = 5 x + 7$

Find the exact value. - $\log \sqrt { 10 }$

Solve the equation. - $3 ( 6 + 3 x ) = \frac { 1 } { 27 }$

Solve the equation. Give an exact solution. - $8 ^ { x } = 13$