Call Now to Set Up Tutoring:

(888) 888-0446

Advanced Geometry : How to graph an exponential function

Study concepts, example questions & explanations for Advanced Geometry

Create An Account

All Advanced Geometry Resources

6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #133 : Advanced Geometry

Give the -coordinate of the -intercept of the graph of the function

$f(x) = 2 \cdot 10 ^{x} - 8$

Possible Answers:

10,000

$\log 4$

Correct answer:

Explanation:

The -intercept of the graph of f(x) is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is f(0) , which can be found by substituting 0 for in the definition:

$f(x) = 2 \cdot 10 ^{x} - 8$

$f(0) = 2 \cdot 10 ^{0} - 8 = 2 \cdot 1 - 8 = 2 - 8 = -6$

Report an Error

Example Question #21 : How To Graph An Exponential Function

Give the -coordinate of the -intercept of the graph of the function $f(x) = 2e^{x}+ 7$ .

Possible Answers:

$\ln \frac{7}{2}$

2e+7

The graph of f(x) has no -intercept.

Correct answer:

Explanation:

The -intercept of the graph of f(x) is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is f(0) , which can be found by substituting 0 for in the definition:

$f(x) = 2e^{x}+ 7$

$f(0) = 2e^{0}+ 7 = 2 \cdot 1 + 7 = 2+7 = 9$ ,

the correct choice.

Report an Error

Example Question #135 : Advanced Geometry

Give the -coordinate of the -intercept of the graph of the function $f(x) = 2e^{x}+ 7$ .

Possible Answers:

The graph of f(x) has no -intercept.

$\ln \frac{7}{2}$

$\frac{7}{2}$

Correct answer:

The graph of f(x) has no -intercept.

Explanation:

The -intercept(s) of the graph of f(x) are the point(s) at which it intersects the -axis. The -coordinate of each is 0,; their -coordinate(s) are those value(s) of for which f(x) = 0 , so set up, and solve for , the equation:

f(x)= 0

$2e^{x}+ 7 = 0$

Subtract 7 from both sides:

$2e^{x}+ 7 - 7 = 0 - 7$

$2e^{x}= - 7$

Divide both sides by 2:

$\frac{2e^{x}}{2}=\frac{ - 7}{2}$

$e^{x} =-\frac{ 7}{2}$

The next step would normally be to take the natural logarithm of both sides in order to eliminate the exponent. However, the negative number $-\frac{ 7}{2}$ does not have a natural logarithm. Therefore, this equation has no solution, and the graph of f(x) has no -intercept.

Report an Error

Example Question #51 : Graphing

Give the -coordinate of the -intercept of the graph of the function

$f(x) = 2 \cdot 10 ^{x} - 8$

Possible Answers:

10,000

$\log 4$

Correct answer:

$\log 4$

Explanation:

f(x)= 0

$2 \cdot 10 ^{x} - 8 = 0$

Add 8 to both sides:

$2 \cdot 10 ^{x} - 8 + 8 = 0 + 8$

$2 \cdot 10 ^{x} = 8$

Divide both sides by 2:

$\frac{2 \cdot 10 ^{x}}{2} =\frac{ 8}{2}$

$10 ^{x} =4$

Take the common logarithm of both sides to eliminate the base:

$\log 10 ^{x} =\log 4$

$x=\log 4$

Report an Error

Example Question #51 : Graphing

Give the domain of the function $f(x) = 2e^{x-3}- 7$ .

Possible Answers:

$\left \{ x|x> -7\right \}$

The set of all real numbers

$\left \{ x|x \ge -7\right \}$

$\left \{ x|x \ge -3\right \}$

$\left \{ x|x> -3\right \}$

Correct answer:

The set of all real numbers

Explanation:

Let $g(x) = e^{x}$ . This function is defined for any real number , so the domain of g(x) is the set of all real numbers. In terms of g(x) ,

f(x) = 2g(x-3) - 7

Since g(x) is defined for all real , so is g(x-3) ; it follows that f(x) is as well. The correct domain is the set of all real numbers.

Report an Error

Example Question #52 : Graphing

Give the range of the function $f(x) = 2e^{x-3}- 7$ .

Possible Answers:

$[-7, \infty )$

$(-7, \infty )$

$[-3, \infty )$

$(-3, \infty )$

The set of all real numbers

Correct answer:

$(-7, \infty )$

Explanation:

Since a positive number raised to any power is equal to a positive number,

$e^{x-3} > 0$

Applying the properties of inequality, we see that

$2 \cdot e^{x-3} > 2 \cdot 0$

$2 e^{x-3} > 0$

$2 e^{x-3} -7 > 0 - 7$

$2 e^{x-3} -7 > - 7$

f(x) > - 7 ,

and the range of f(x) is the set $(-7, \infty )$ .

Report an Error

View Tutors

Uzma
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Biology, General. The University of Texas at Dallas, Master of Scienc...

View Tutors

Jaahanava
Certified Tutor

University of Windsor, Master's/Graduate, Computer Science .

View Tutors

Georges Frederic Agustin
Certified Tutor

Boston College, Bachelor in Arts, History. University of Arizona, Master of Arts, History.

All Advanced Geometry Resources

6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Denver, Algebra Tutors in Miami, LSAT Tutors in Philadelphia, Computer Science Tutors in Atlanta, English Tutors in Seattle, LSAT Tutors in San Diego, MCAT Tutors in San Diego, ACT Tutors in San Diego, ACT Tutors in Philadelphia, GMAT Tutors in Seattle

Popular Courses & Classes

MCAT Courses & Classes in Chicago, LSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Miami, ISEE Courses & Classes in Denver, GRE Courses & Classes in Denver, GMAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Philadelphia, Spanish Courses & Classes in Denver

Popular Test Prep

SAT Test Prep in Phoenix, ISEE Test Prep in Chicago, SAT Test Prep in Boston, ACT Test Prep in Philadelphia, GMAT Test Prep in Philadelphia, SSAT Test Prep in Boston, MCAT Test Prep in Phoenix, SAT Test Prep in Denver, SSAT Test Prep in Houston, MCAT Test Prep in Dallas Fort Worth

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

Advanced Geometry : How to graph an exponential function

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #133 : Advanced Geometry

Example Question #21 : How To Graph An Exponential Function

Example Question #135 : Advanced Geometry

Example Question #51 : Graphing

Example Question #51 : Graphing

Example Question #52 : Graphing

All Advanced Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: