Question 1

Use the power property to rewrite the expression.
-$\log _ { \mathrm { x } } \mathrm { y } ^ { \mathrm { z } }$

Accepted Answer

A)  $z \log _ { y } x$ 
B)  $y \log _ { x } z$ 
C)  $z \log _ { x } y$ 
D)  $x \log _ { y } z$ 
A)  $z \log _ { y } x$ 
B)  $y \log _ { x } z$ 
C)  $z \log _ { x } y$ 
D)  $x \log _ { y } z$

Question 2

For the given functions f and g, find the composition.
-$f ( x ) = 4 x + 5 ; g ( x ) = 2 x - 1 \quad$ Find $( f \circ g ) ( x )$

Accepted Answer

A)  $8 x + 1$ 
B)  $8 x + 9$ 
C)  $8 X + 9$ 
D)  $8 x + 4$ 
A)  $8 x + 1$ 
B)  $8 x + 9$ 
C)  $8 X + 9$ 
D)  $8 x + 4$

Question 3

Simplify.
-$\log _2 { 2 ^ { 17}}$

Accepted Answer

A)  2 
B)  $\log _ { 2 } 17$ 
C)  19 
D)  17 
A)  2 
B)  $\log _ { 2 } 17$ 
C)  19 
D)  17

Question 4

Graph the function.
-$f(x)=\log x-2$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

Question 5

Determine whether the graph of the function is the graph of a one-to-one function.
-

Accepted Answer

A) True 
 B)False

Question 6

Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x + 7 } \
F ( x ) = \sqrt { - 6 x + 7 }
\end{array}$

Accepted Answer

A)  $F ( x ) = ( f \circ h ) ( x )$ 
B)  $F ( x ) = ( g \circ h ) ( x )$ 
C)  $F ( x ) = ( h \circ f ) ( x )$ 
D)  $F ( x ) = ( h \circ g ) ( x )$ 
A)  $F ( x ) = ( f \circ h ) ( x )$ 
B)  $F ( x ) = ( g \circ h ) ( x )$ 
C)  $F ( x ) = ( h \circ f ) ( x )$ 
D)  $F ( x ) = ( h \circ g ) ( x )$

Question 7

For the given functions f and g, find the requested function.
-If $f ( x ) = x ^ { 2 } + 4 x$ and $g ( x ) = x + 2$, find $( g \circ f ) ( 2 )$.

Accepted Answer

A)  48 
B)  16 
C)  14 
D)  32 
A)  48 
B)  16 
C)  14 
D)  32

Question 8

For the given functions f and g, find the composition.
-$f ( x ) = x ^ { 2 } - 6 x + 3 ; g ( x ) = \sqrt { x } \quad$ Find $( f \circ g ) ( 9 )$

Accepted Answer

A)  $- 12$ 
B)  $- 15$ 
C)  $- 6$ 
D)  $- 9$ 
A)  $- 12$ 
B)  $- 15$ 
C)  $- 6$ 
D)  $- 9$

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

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

Accepted Answer

A)  6 
B)  5 
C)  9 
D)  8 
A)  6 
B)  5 
C)  9 
D)  8

Question 11

Given the values of f and g, find the function value.
-$f ( 19 ) = 14 ; g ( 19 ) = 5 \quad$ Find $( f - g ) ( 19 )$

Accepted Answer

A)  13 
B)  $- 10$ 
C)  19 
D)  9 
A)  13 
B)  $- 10$ 
C)  19 
D)  9

Question 12

Determine whether the function is a one-to-one function.
-

Accepted Answer

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

Question 13

Solve. Round the answer to the nearest whole number.
-The size of the coyote population at a national park increases at the rate of $4.8 \%$ per year. If the size of the current population is 149 , find how many coyotes there will be in 7 years.

Accepted Answer

A)  205 coyotes 
B)  209 coyotes 
C)  207 coyotes 
D)  211 coyotes 
A)  205 coyotes 
B)  209 coyotes 
C)  207 coyotes 
D)  211 coyotes

Question 14

Use a calculator to approximate the natural logarithm to four decimal places.
-$\ln 24$

Accepted Answer

A)  $0.3137$ 
B)  $1.3802$ 
C)  $8.8561$ 
D)  $3.1781$ 
A)  $0.3137$ 
B)  $1.3802$ 
C)  $8.8561$ 
D)  $3.1781$

Question 15

Solve the equation.
-$\log _ { 9 } x ^ { 2 } = 4$

Accepted Answer

A)  6561 
B)  512 
C)  $81 , - 81$ 
D)  $6 , - 6$ 
A)  6561 
B)  512 
C)  $81 , - 81$ 
D)  $6 , - 6$

Question 16

Graph the function and its inverse on the same set of axes.
-$f ( x ) = \frac { 1 } { 2 } x - 4$

Accepted Answer

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

Question 17

Solve the equation.
-$\log _ { 2 } 3 + \log _ { 2 } x = 1$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $\sqrt [ 3 ] { 2 }$ 
D)  $\frac { 2 } { 3 }$ 
A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $\sqrt [ 3 ] { 2 }$ 
D)  $\frac { 2 } { 3 }$

Question 18

Graph the exponential function.
-$f(x)=5^{x}+1$

Accepted Answer

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

Question 19

Solve the equation.
-$5 ^ { x } = 125$

Accepted Answer

A)  2 
B)  25 
C)  3 
D)  4 
A)  2 
B)  25 
C)  3 
D)  4

Question 20

Use the following approximations to find the approximate value of the logarithmic expression: 
$\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$
$\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$
-$\log _ { b } \sqrt { 3 }$ (Round answer to nearest hundredth.)

Accepted Answer

A)  $0.71$ 
B)  1 
C)  $0.25$ 
D)  $1.73$ 
A)  $0.71$ 
B)  1 
C)  $0.25$ 
D)  $1.73$

Use the power property to rewrite the expression. - $\log _ { \mathrm { x } } \mathrm { y } ^ { \mathrm { z } }$

For the given functions f and g, find the composition. - $f ( x ) = 4 x + 5 ; g ( x ) = 2 x - 1 \quad$ Find $( f \circ g ) ( x )$

Simplify. - $\log _2 { 2 ^ { 17}}$

Graph the function. - $f(x)=\log x-2$ $Graph the function. - f(x)=\log x-2$

Determine whether the graph of the function is the graph of a one-to-one function. -

Write the function F(x) as a composition of f, g, or h. - f(x)=-2g(x)=-6xh(x)= F(x)=

For the given functions f and g, find the requested function. -If $f ( x ) = x ^ { 2 } + 4 x$ and $g ( x ) = x + 2$ , find $( g \circ f ) ( 2 )$ .

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 2 } - 6 x + 3 ; g ( x ) = \sqrt { x } \quad$ Find $( f \circ g ) ( 9 )$

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

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

Given the values of f and g, find the function value. - $f ( 19 ) = 14 ; g ( 19 ) = 5 \quad$ Find $( f - g ) ( 19 )$

Determine whether the function is a one-to-one function. -

Solve. Round the answer to the nearest whole number. -The size of the coyote population at a national park increases at the rate of $4.8 \%$ per year. If the size of the current population is 149 , find how many coyotes there will be in 7 years.

Use a calculator to approximate the natural logarithm to four decimal places. - $\ln 24$

Solve the equation. - $\log _ { 9 } x ^ { 2 } = 4$

Graph the function and its inverse on the same set of axes. - $f ( x ) = \frac { 1 } { 2 } x - 4$ $Graph the function and its inverse on the same set of axes. - f ( x ) = \frac { 1 } { 2 } x - 4$

Solve the equation. - $\log _ { 2 } 3 + \log _ { 2 } x = 1$

Graph the exponential function. - $f(x)=5^{x}+1$ $Graph the exponential function. - f(x)=5^{x}+1$

Solve the equation. - $5 ^ { x } = 125$

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5 \quad \log _ { b } 8 \approx 0.9$ $\log _ { b } 5 \approx 0.7 \quad \log _ { b } 20 \approx 1.3$ - $\log _ { b } \sqrt { 3 }$ (Round answer to nearest hundredth.)

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Exponential and Logarithmic Functions

Use the power property to rewrite the expression. - log⁡xyz\log _ { \mathrm { x } } \mathrm { y } ^ { \mathrm { z } }logx​yz

For the given functions f and g, find the composition. - f(x)=4x+5;g(x)=2x−1f ( x ) = 4 x + 5 ; g ( x ) = 2 x - 1 \quadf(x)=4x+5;g(x)=2x−1 Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Simplify. - log⁡2217\log _2 { 2 ^ { 17}}log2​217

Graph the function. - f(x)=log⁡x−2f(x)=\log x-2f(x)=logx−2