Question 1

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a.
-

Accepted Answer

A) Exponential;   
B) Exponential;   
C) Exponential; a = 9 
D) Not exponential 
A) Exponential;   
B) Exponential;   
C) Exponential; a = 9 
D) Not exponential

Question 2

Write the word or phrase that best completes each statement or answers the question.
-The surface area S (in square inches)of a cylindrical pipe with length 12 inches is given by   πr, where r is the radius of the piston (in inches). If the radius is increasing with time t (in minutes)according to the formula   , find the surface area S of the pipe as a function of the time t.

Accepted Answer

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

Question 3

For the given functions f and g, find the requested composite function.
-f(x)= -2x + 5, g(x)= 5x + 3; Find (g ∘ f)(x).

Accepted Answer

A) -10x + 28 
B) -10x + 11 
C) 10x + 28 
D) -10x - 22 
A) -10x + 28 
B) -10x + 11 
C) 10x + 28 
D) -10x - 22

Question 4

Approximate the value using a calculator. Express answer rounded to three decimal places.
-

Accepted Answer

A) 82.991 
B) 71.499 
C) 12.155 
D) 41.083 
A) 82.991 
B) 71.499 
C) 12.155 
D) 41.083

Question 5

For the given functions f and g, find the requested composite function.
-f(x)=   , g(x)= 4x - 3; Find (g ∘ f)(x).

Accepted Answer

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

Question 6

The function f is one-to-one. Find its inverse.
-

Accepted Answer

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

Question 7

Find the domain of the composite function f ∘ g.
-f(x)= x + 4; g(x)=

Accepted Answer

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

Question 8

The graph of a one-to-one function f is given. Draw the graph of the inverse function f   as a dashed line or curve.
-

Accepted Answer

A)    
B)    
A)    
B)

Question 9

Write the word or phrase that best completes each statement or answers the question.
-If   and g(x)= 2x - a, find a so that the graph of f ∘ g crosses the y-axis at 36.

Accepted Answer

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

Question 10

Solve the problem.
-The bacteria in a 8-liter container double every 3 minutes. After 54 minutes the container is full. How longdid it take to fill a quarter of the container?

Accepted Answer

A) 48 min 
B) 13.5 min 
C) 40.5 min 
D) 27 min 
A) 48 min 
B) 13.5 min 
C) 40.5 min 
D) 27 min

Question 11

Change the logarithmic expression to an equivalent expression involving an exponent.
-

Accepted Answer

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

Question 12

Write the word or phrase that best completes each statement or answers the question.
-Instruments on a satellite measure the amount of power generated by the satelliteʹs power supply. Thetime t and the power P can be modeled by the function   where t is in days and P is in watts.How much power will be available after 378 days? Round to the nearest hundredth.

Accepted Answer

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

Question 13

For the given functions f and g, find the requested composite function value.
-  , g(x)= 16x - 3; Find (f ∘ g)(7).

Accepted Answer

A) 106,602 
B) 6,717 
C) 99,885 
D) 45,780 
A) 106,602 
B) 6,717 
C) 99,885 
D) 45,780

Question 14

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The accompanying tables represent a function f that converts seconds to hours and a function g thatconverts hours to days.

Accepted Answer

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

Question 15

Decide whether or not the functions are inverses of each other.
-  , domain     domain

Accepted Answer

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

Question 16

Change the exponential expression to an equivalent expression involving a logarithm.
-

Accepted Answer

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

Question 17

The function f is one-to-one. Find its inverse.
-

Accepted Answer

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

Question 18

Solve the equation.
-

Accepted Answer

A) {2} 
B) {4} 
C) {3} 
D) {1} 
A) {2} 
B) {4} 
C) {3} 
D) {1}

Question 19

Find the domain of the composite function f ∘ g.
-f(x)=   g(x)= 2x + 4

Accepted Answer

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

Question 20

Solve the problem.
-Suppose that   . What is f(2)? What point is on the graph of f?

Accepted Answer

A) 7; (2, 7) 
B) 4; (2, 4) 
C) 4; (3, 4) 
D) 7; (2, 4) 
A) 7; (2, 7) 
B) 4; (2, 4) 
C) 4; (3, 4) 
D) 7; (2, 4)

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. -

For the given functions f and g, find the requested composite function. -f(x)= -2x + 5, g(x)= 5x + 3; Find (g ∘ f)(x).

Approximate the value using a calculator. Express answer rounded to three decimal places. -

For the given functions f and g, find the requested composite function. -f(x)= , g(x)= 4x - 3; Find (g ∘ f)(x).

The function f is one-to-one. Find its inverse. -

Find the domain of the composite function f ∘ g. -f(x)= x + 4; g(x)=

The graph of a one-to-one function f is given. Draw the graph of the inverse function f as a dashed line or curve. -

Write the word or phrase that best completes each statement or answers the question. -If and g(x)= 2x - a, find a so that the graph of f ∘ g crosses the y-axis at 36.

Solve the problem. -The bacteria in a 8-liter container double every 3 minutes. After 54 minutes the container is full. How longdid it take to fill a quarter of the container?

Change the logarithmic expression to an equivalent expression involving an exponent. -

For the given functions f and g, find the requested composite function value. - , g(x)= 16x - 3; Find (f ∘ g)(7).

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -The accompanying tables represent a function f that converts seconds to hours and a function g thatconverts hours to days.

Decide whether or not the functions are inverses of each other. - , domain domain

Change the exponential expression to an equivalent expression involving a logarithm. -

The function f is one-to-one. Find its inverse. -

Solve the equation. -

Find the domain of the composite function f ∘ g. -f(x)= g(x)= 2x + 4

Solve the problem. -Suppose that . What is f(2)? What point is on the graph of f?

Equations and Inequalities

Graphs

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Graphing Utilities

Filters

Exam 6: Exponential and Logarithmic Functions

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. -

For the given functions f and g, find the requested composite function. -f(x)= -2x + 5, g(x)= 5x + 3; Find (g ∘ f)(x).

Approximate the value using a calculator. Express answer rounded to three decimal places. -

For the given functions f and g, find the requested composite function. -f(x)= , g(x)= 4x - 3; Find (g ∘ f)(x).

The function f is one-to-one. Find its inverse. -

Find the domain of the composite function f ∘ g. -f(x)= x + 4; g(x)=

The graph of a one-to-one function f is given. Draw the graph of the inverse function f as a dashed line or curve. -

Write the word or phrase that best completes each statement or answers the question. -If and g(x)= 2x - a, find a so that the graph of f ∘ g crosses the y-axis at 36.

Solve the problem. -The bacteria in a 8-liter container double every 3 minutes. After 54 minutes the container is full. How longdid it take to fill a quarter of the container?

Change the logarithmic expression to an equivalent expression involving an exponent. -

For the given functions f and g, find the requested composite function value. - , g(x)= 16x - 3; Find (f ∘ g)(7).

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -The accompanying tables represent a function f that converts seconds to hours and a function g thatconverts hours to days.

Decide whether or not the functions are inverses of each other. - , domain domain

Change the exponential expression to an equivalent expression involving a logarithm. -

The function f is one-to-one. Find its inverse. -

Solve the equation. -

Find the domain of the composite function f ∘ g. -f(x)= g(x)= 2x + 4

Solve the problem. -Suppose that . What is f(2)? What point is on the graph of f?

Equations and Inequalities

Graphs

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Graphing Utilities

Filters