Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Graph Exponential Functions

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Graph Exponential Functions

Choose the description below that matches the equation:

y = 2^x

Possible Answers:

Exponential growth

Y-intercept at y=1

Exponential growth

Y-intercept at y=2

Exponential decay

Y-intercept at y = 1

Exponential decay

Y-intercept at y = 0

Exponential growth

Y-intercept at y = 0

Correct answer:

Exponential growth

Y-intercept at y=1

Explanation:

Exponential graphs can either decay or grow. This is based on the value of the base of the exponent. If the base is greater than , the graph will be growth. And, if the base is less than , then the graph will be decay. In this situation, our base is . Since this is greater than , we have a growth graph. Then, to determine the y-intercept we substitute x=0 . Thus, we get:

y = 2^0 = 1 for the y-intercept.

Report an Error

Example Question #2 : Graph Exponential Functions

Choose the description that matches the equation below:

$y = (\frac{1}{3})^{4x}$

Possible Answers:

Exponential growth

y = 3

Exponential decay

y = 1

Exponential decay

$y = \frac{1}{3}$

Exponential decay

y = 0

Exponential growth

y = 1

Correct answer:

Exponential decay

y = 1

Explanation:

Exponential graphs can either decay or grow. This is based on the value of the base of the exponent. If the base is greater than , the graph will be growth. And, if the base is less than , then the graph will be decay. In this situation, our base is $\frac{1}{3}$ . Since this is less than , we have a decay graph. Then, to determine the y-intercept we substitute x=0 . Thus, we get:

$y = (\frac{1}{3})^{(4\cdot 0)} = (\frac{1}{3})^0=1$ for the y-intercept.

Report an Error

Example Question #1 : Graph Exponential Functions

Which of the following represents the graph of -(2^x) ?

Possible Answers:

Graph1

Graph4

Graph2

Graph3

Correct answer:

Graph1

Explanation:

Note that the negative sign in this function comes outside of the parentheses. This should show you that the bigger the number in parentheses, the lower the curve of the graph will go. Since this is an exponential function, the larger that the x value gets, then, the "more negative" this graph will go. The graph closest to zero on the left-hand side - where x is negative - and then shoots down and to the right rapidly when x gets larger is the correct graph.

Report an Error

Example Question #131 : Exponential And Logarithmic Functions

Define a function as follows:

$f(x) = 4 ^{x+2} - 3$

Give the -intercept of the graph of .

Possible Answers:

(0,-3)

$\left ( 0, \frac{3}{4}\right )$

(0,1)

(0,2)

(0,13)

Correct answer:

(0,13)

Explanation:

The -coordinate ofthe -intercept of the graph of is 0, and its -coordinate is f(0) :

$f(x) = 4 ^{x+2} - 3$

$f(0) = 4 ^{0+2} - 3 = 4 ^{2} - 3 = 16 - 3 = 13$

The -intercept is the point (0,13) .

Report an Error

Example Question #4 : Graph Exponential Functions

Does the function $y = 4^{x}$ have any -intercepts?

Possible Answers:

Yes, x = 1

Yes, x = 4 and x = -4

Yes, x = 0

That cannot be determined from the information given.

Correct answer:

Explanation:

The -intercept of a function is where y = 0 . Thus, we are looking for the -value which makes $0 = 4^{x}$ .

If we try to solve this equation for we get an error.

To bring the exponent down we will need to take the natural log of both sides.

ln(0)=xln(4)

Since the natural log of zero does not exist, there is no exponent which makes this equation true.

Thus, there is no -intercept for this function.

Report an Error

Example Question #10 : Graphing Exponential Functions

Which of the following functions represents exponential decay?

Possible Answers:

$y = 6^{x + 3}$

$y = \left(\frac{1}{3}\right)^{x}$

$y = 3(2^{x})$

$y = (-2)^{x}$

$y = 5^{x}$

Correct answer:

$y = \left(\frac{1}{3}\right)^{x}$

Explanation:

Exponential decay describes a function that decreases by a factor every time increases by .

These can be recognizable by those functions with a base which is between and .

The general equation for exponential decay is,

A=A_0b^t where the base is represented by and 0<b<1 .

Thus, we are looking for a fractional base.

The only function that has a fractional base is,

$y = \left(\frac{1}{3}\right)^{x}$ .

Report an Error

Example Question #8 : Graphing Exponential Functions

What is the -intercept of $y = 4(2^{x})$ ?

Possible Answers:

There is no -intercept.

Correct answer:

Explanation:

The -intercept of a graph is the point on the graph where the -value is .

Thus, to find the -intercept, substitute x = 0 and solve for .

Thus, we get:

$y = 4(2^{0}) = 4(1)=4$

Report an Error

View Pre-Calculus Tutors

Susana I
Certified Tutor

California State Polytechnic University-Pomona, Bachelor of Science, Geology. The University of Texas at El Paso, Master of S...

View Pre-Calculus Tutors

Aashish
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Biological and Physical Sciences. University of Toledo, Doctor of M...

View Pre-Calculus Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Los Angeles, Chemistry Tutors in San Diego, ISEE Tutors in Dallas Fort Worth, French Tutors in San Diego, GMAT Tutors in Boston, ISEE Tutors in Chicago, LSAT Tutors in Philadelphia, English Tutors in Seattle, Statistics Tutors in San Francisco-Bay Area, French Tutors in Denver

Popular Courses & Classes

SAT Courses & Classes in Houston, GMAT Courses & Classes in Seattle, GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Atlanta, ACT Courses & Classes in Boston, ISEE Courses & Classes in Los Angeles, ISEE Courses & Classes in Washington DC, SAT Courses & Classes in Phoenix, GMAT Courses & Classes in Philadelphia, GRE Courses & Classes in New York City

Popular Test Prep

ACT Test Prep in Miami, MCAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Atlanta, GRE Test Prep in Chicago, GMAT Test Prep in Boston, GMAT Test Prep in Denver, SAT Test Prep in Dallas Fort Worth, ACT Test Prep in Los Angeles, GRE Test Prep in Dallas Fort Worth, LSAT Test Prep in Boston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Precalculus : Graph Exponential Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Graph Exponential Functions

Example Question #2 : Graph Exponential Functions

Example Question #1 : Graph Exponential Functions

Example Question #131 : Exponential And Logarithmic Functions

Example Question #4 : Graph Exponential Functions

Example Question #10 : Graphing Exponential Functions

Example Question #8 : Graphing Exponential Functions

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: