Question 1

Write the word or phrase that best completes each statement or answers the question.
-Why canʹt 1 be the base of a logarithmic function?

Accepted Answer

Answers may vary. One possibility: If th

Question 2

Graph the exponential function using transformations where appropriate.
-$f(x)=-2 x$

Accepted Answer

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

Question 3

Determine whether or not the function is one-to-one.
-

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 4

Solve the equation. Give the answer in exact form.
-$$6 ^ { 2 x } - 4 \left( 6 ^ { x } \right) = 32$$

Accepted Answer

A)  $\{ 6 \ln 8,6 \ln ( - 4 ) \}$ 
B)  $\{ 6 \ln 8 \}$ 
C)  $\left\{ \log _ { 6 } 8 , \log _ { 6 } ( - 4 ) \right\}$ 
D)  $\left\{ \log _ { 6 } 8 \right\}$ 
A)  $\{ 6 \ln 8,6 \ln ( - 4 ) \}$ 
B)  $\{ 6 \ln 8 \}$ 
C)  $\left\{ \log _ { 6 } 8 , \log _ { 6 } ( - 4 ) \right\}$ 
D)  $\left\{ \log _ { 6 } 8 \right\}$

Question 5

Solve the problem.
-Quail are game birds that fare poorly when their habitat is encroached upon. Wildlife biologists have discovered that the population P of quail in a region is related to the percent of the region
That has been paved with roads and parking lots, according to the formula $$\mathrm { P } = \mathrm { k } \ln \left( \frac { 30 } { \mathrm { x } + 5 } \right) , 0 \leq \mathrm { x } \leq 25$$ where x is the percent of the region that has been paved. For a particular rural region, P = 1600
When x = 0. Predict what the quail population will be in this region when it becomes 5% paved.
Round your answer to the nearest whole number.

Accepted Answer

A)  0 quail 
B)  1034 quail 
C)  981 quail 
D)  992 quail 
A)  0 quail 
B)  1034 quail 
C)  981 quail 
D)  992 quail

Question 6

Provide an appropriate response.
-$$\text { Explain how the graph of } y = - 4 \left( \frac { 1 } { 3 } \right) ^ { x } \text { can be obtained from the graph of } y = 3 ^ { x }$$

Accepted Answer

The graph is reflected over th

Question 7

Determine whether the statement is true or false.
-If a function f has an inverse and $f ( 1 ) = - 3 , \text { then } f ^ { - 1 } ( - 3 ) = 1$

Accepted Answer

A) True 
 B)False

Question 8

Write the word or phrase that best completes each statement or answers the question.
-Give a definition for the following term: Exponential function .

Accepted Answer

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

Question 9

Determine whether or not the function is one-to-one.
-$$f ( x ) = 164 - x ^ { 2 }$$

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 10

Write the word or phrase that best completes each statement or answers the question.
-What is the range of the function $y = \log _ { 9 } x$ ?

Accepted Answer

A)  $[ 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( 9 , \infty )$ 
A)  $[ 0 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( 9 , \infty )$

Question 11

Decide whether the pair of functions graphed are inverses.
-

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 12

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log \mathrm { b } \left( \frac { m ^ { 5 } p ^ { 2 } } { n ^ { 4 } b ^ { 8 } } \right)$

Accepted Answer

A)  $5 \log _ { b } m + 2 \log _ { b } p - 4 \log _ { b } n - 8$ 
B)  $m ^ { 5 } p ^ { 2 } - n ^ { 4 } b ^ { 8 }$ 
C)  $5 \log _ { b } m + 2 \log _ { b } p - 4 \log _ { b } n + 8$ 
D)  $\log _ { b } m ^ { 5 } + \log _ { b } p ^ { 2 } + \log _ { b } n ^ { 4 } - \log b b ^ { 8 }$ 
A)  $5 \log _ { b } m + 2 \log _ { b } p - 4 \log _ { b } n - 8$ 
B)  $m ^ { 5 } p ^ { 2 } - n ^ { 4 } b ^ { 8 }$ 
C)  $5 \log _ { b } m + 2 \log _ { b } p - 4 \log _ { b } n + 8$ 
D)  $\log _ { b } m ^ { 5 } + \log _ { b } p ^ { 2 } + \log _ { b } n ^ { 4 } - \log b b ^ { 8 }$

Question 13

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to solve the problem.
-The function defined by f(x) = 3x - 4 was used to encode a message as:
38 11 62 11 50 -1 17 -1 23 38
Find the inverse function and determine the message.

Accepted Answer

The answer of Use the alphabet coding method (A =1,...

Question 14

Determine whether or not the function is one-to-one.
-

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 15

Match the function with its graph.
-$$f ( x ) = \log _ { 4 } ( x - 1 )$$

Accepted Answer

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

Question 16

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-7(x + 1) = 45.00

Accepted Answer

A)  {1.96} 
B)  {0.96} 
C)  {6.41} 
D)  {2.96} 
A)  {1.96} 
B)  {0.96} 
C)  {6.41} 
D)  {2.96}

Question 17

Solve for the indicated variable.
-$$A = \frac { B s } { 1 - ( 1 + z ) ^ { - t ^ { \prime } } } \text { for } t$$

Accepted Answer

A)  $t = \frac { \ln A - \ln ( A - B s ) } { \ln ( 1 + z ) }$ 
B)  $t = \frac { \ln B } { \ln [ ( A - A s ) ( 1 - z ) ] }$ 
C)  $t = \ln \frac { B } { ( A - A s ) ( 1 + z ) }$ 
D)  $t = \ln \frac { A } { ( A - B s ) ( 1 + z ) }$ 
A)  $t = \frac { \ln A - \ln ( A - B s ) } { \ln ( 1 + z ) }$ 
B)  $t = \frac { \ln B } { \ln [ ( A - A s ) ( 1 - z ) ] }$ 
C)  $t = \ln \frac { B } { ( A - A s ) ( 1 + z ) }$ 
D)  $t = \ln \frac { A } { ( A - B s ) ( 1 + z ) }$

Question 18

Evaluate the logarithm.
-$\log _ { 1 / 5 } 5$

Accepted Answer

A)  $- 1$ 
B)  2 
C)  $- 2$ 
D)  1 
A)  $- 1$ 
B)  2 
C)  $- 2$ 
D)  1

Question 19

Determine whether or not the function is one-to-one.
-$$f ( x ) = - 3.04$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 20

Find the function value. If the result is irrational, round your answer to the nearest thousandth.
-Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$. Find $f ( - 3 )$.

Accepted Answer

A)  $- \frac { 1 } { 216 }$ 
B)  $\frac { 1 } { 216 }$ 
C)  216 
D)  $- 18$ 
A)  $- \frac { 1 } { 216 }$ 
B)  $\frac { 1 } { 216 }$ 
C)  216 
D)  $- 18$

Write the word or phrase that best completes each statement or answers the question. -Why canʹt 1 be the base of a logarithmic function?

Graph the exponential function using transformations where appropriate. - $f(x)=-2 x$

Determine whether or not the function is one-to-one. -

Solve the equation. Give the answer in exact form. - $6 ^ { 2 x } - 4 \left( 6 ^ { x } \right) = 32$

Provide an appropriate response. - $\text { Explain how the graph of } y = - 4 \left( \frac { 1 } { 3 } \right) ^ { x } \text { can be obtained from the graph of } y = 3 ^ { x }$

Determine whether the statement is true or false. -If a function f has an inverse and $f ( 1 ) = - 3 , \text { then } f ^ { - 1 } ( - 3 ) = 1$

Write the word or phrase that best completes each statement or answers the question. -Give a definition for the following term: Exponential function .

Determine whether or not the function is one-to-one. - $f ( x ) = 164 - x ^ { 2 }$

Write the word or phrase that best completes each statement or answers the question. -What is the range of the function $y = \log _ { 9 } x$ ?

Decide whether the pair of functions graphed are inverses. -

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log \mathrm { b } \left( \frac { m ^ { 5 } p ^ { 2 } } { n ^ { 4 } b ^ { 8 } } \right)$

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to solve the problem. -The function defined by f(x) = 3x - 4 was used to encode a message as: 38 11 62 11 50 -1 17 -1 23 38 Find the inverse function and determine the message.

Determine whether or not the function is one-to-one. -

Match the function with its graph. - $f ( x ) = \log _ { 4 } ( x - 1 )$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. -7(x + 1) = 45.00

Solve for the indicated variable. - $A = \frac { B s } { 1 - ( 1 + z ) ^ { - t ^ { \prime } } } \text { for } t$

Evaluate the logarithm. - $\log _ { 1 / 5 } 5$

Determine whether or not the function is one-to-one. - $f ( x ) = - 3.04$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$ . Find $f ( - 3 )$ .

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 4: Inverse, Exponential, and Logarithmic Functions

Write the word or phrase that best completes each statement or answers the question. -Why canʹt 1 be the base of a logarithmic function?

Graph the exponential function using transformations where appropriate. - f(x)=−2xf(x)=-2 xf(x)=−2x

Determine whether or not the function is one-to-one. -

Solve the equation. Give the answer in exact form. - 62x−4(6x)=326 ^ { 2 x } - 4 \left( 6 ^ { x } \right) = 3262x−4(6x)=32

Determine whether the statement is true or false. -If a function f has an inverse and f(1)=−3, then f−1(−3)=1f ( 1 ) = - 3 , \text { then } f ^ { - 1 } ( - 3 ) = 1f(1)=−3, then f−1(−3)=1

Write the word or phrase that best completes each statement or answers the question. -Give a definition for the following term: Exponential function .

Determine whether or not the function is one-to-one. - f(x)=164−x2f ( x ) = 164 - x ^ { 2 }f(x)=164−x2

Write the word or phrase that best completes each statement or answers the question. -What is the range of the function y=log⁡9xy = \log _ { 9 } xy=log9​x ?

Decide whether the pair of functions graphed are inverses. -

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - log⁡b(m5p2n4b8)\log \mathrm { b } \left( \frac { m ^ { 5 } p ^ { 2 } } { n ^ { 4 } b ^ { 8 } } \right)logb(n4b8m5p2​)

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to solve the problem. -The function defined by f(x) = 3x - 4 was used to encode a message as: 38 11 62 11 50 -1 17 -1 23 38 Find the inverse function and determine the message.

Determine whether or not the function is one-to-one. -

Match the function with its graph. - f(x)=log⁡4(x−1)f ( x ) = \log _ { 4 } ( x - 1 )f(x)=log4​(x−1)

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. -7(x + 1) = 45.00

Solve for the indicated variable. - A=Bs1−(1+z)−t′ for tA = \frac { B s } { 1 - ( 1 + z ) ^ { - t ^ { \prime } } } \text { for } tA=1−(1+z)−t′Bs​ for t

Evaluate the logarithm. - log⁡1/55\log _ { 1 / 5 } 5log1/5​5

Determine whether or not the function is one-to-one. - f(x)=−3.04f ( x ) = - 3.04f(x)=−3.04

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let f(x)=(16)xf ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }f(x)=(61​)x . Find f(−3)f ( - 3 )f(−3) .

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Graph the exponential function using transformations where appropriate. - $f(x)=-2 x$

Solve the equation. Give the answer in exact form. - $6 ^ { 2 x } - 4 \left( 6 ^ { x } \right) = 32$

Determine whether the statement is true or false. -If a function f has an inverse and $f ( 1 ) = - 3 , \text { then } f ^ { - 1 } ( - 3 ) = 1$

Determine whether or not the function is one-to-one. - $f ( x ) = 164 - x ^ { 2 }$

Write the word or phrase that best completes each statement or answers the question. -What is the range of the function $y = \log _ { 9 } x$ ?

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log \mathrm { b } \left( \frac { m ^ { 5 } p ^ { 2 } } { n ^ { 4 } b ^ { 8 } } \right)$

Match the function with its graph. - $f ( x ) = \log _ { 4 } ( x - 1 )$

Solve for the indicated variable. - $A = \frac { B s } { 1 - ( 1 + z ) ^ { - t ^ { \prime } } } \text { for } t$

Evaluate the logarithm. - $\log _ { 1 / 5 } 5$

Determine whether or not the function is one-to-one. - $f ( x ) = - 3.04$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$ . Find $f ( - 3 )$ .