We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Advanced Geometry : Graphing

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 #141 : Coordinate Geometry

Define a function as follows:

$f(x) = 3 ^{x-3}- 9$

Give the -intercept of the graph of .

Possible Answers:

(3,0)

(12,0)

(9,0)

(5,0)

The graph of has no -intercept.

Correct answer:

(5,0)

Explanation:

Since the -intercept is the point at which the graph of intersects the -axis, the -coordinate is 0, and the -coordinate can be found by setting f(x) equal to 0 and solving for . Therefore, we need to find such that

$3 ^{x-3}- 9 = 0$ .

$3 ^{x-3}= 9$

$3 ^{x-3}= 3 ^{2}$

x-3 = 2

x = 5

The -intercept is therefore (5,0) .

Report an Error

Example Question #3 : Graphing

Define a function as follows:

$f(x) = 2 ^{x-1} + 7$

Give the horizontal aysmptote of the graph of .

Possible Answers:

y = 2

y = 1

y = 7

$y = -\frac{7}{2}$

y = 0

Correct answer:

y = 7

Explanation:

The horizontal asymptote of an exponential function can be found by noting that a positive number raised to any power must be positive. Therefore, $2 ^{x-1} > 0$ and $y= 2 ^{x-1} + 7 > 7$ for all real values of . The graph will never crosst the line of the equatin y = 7 , so this is the horizontal asymptote.

Report an Error

Example Question #2 : Graphing

Define functions and as follows:

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

$g(x) = 4^{x-1}$

Give the $y \,$ -coordinate of the point of intersection of their graphs.

Possible Answers:

Correct answer:

Explanation:

First, we rewrite both functions with a common base:

$f(x) = 2^{x +2}$ is left as it is.

$g(x) = 4^{x-1}$ can be rewritten as

$g(x) = \left (2 ^{2} \right )^{x-1}$

$g(x) = 2 ^{2 (x-1)}$

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

To find the point of intersection of the graphs of the functions, set

f(x) = g(x)

$2^{x +2}= 2 ^{2x-2}$

The powers are equal and the bases are equal, so we can set the exponents equal to each other and solve:

x+ 2= 2x-2

x+ 2 -x +2= 2x-2 -x +2

x = 4

To find the $y\,$ -coordinate, substitute 4 for in either definition:

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

$f(4) = 2^{4+2}= 2^{6} = 64$ , the correct response.

Report an Error

Example Question #4 : Graphing

Define a function as follows:

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

Give the -intercept of the graph of .

Possible Answers:

(0,13)

(0,-3)

(0,2)

(0,1)

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

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 #1 : How To Graph An Exponential Function

Define functions and as follows:

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

$g(x) =\left ( \frac{1}{9} \right )^{x-1}$

Give the $y \,$ -coordinate of the point of intersection of their graphs.

Possible Answers:

$\sqrt{3}$

$9\sqrt{3}$

$3\sqrt{3}$

Correct answer:

Explanation:

First, we rewrite both functions with a common base:

$f(x) = 3^{x +2}$ is left as it is.

$g(x) =\left ( \frac{1}{9} \right )^{x-1}$ can be rewritten as

$g(x) =\left ( 3^{-2} \right )^{x-1}$

$g(x) = 3^{-2 (x-1)}$

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

To find the point of intersection of the graphs of the functions, set

f(x) = g(x)

$3^{x +2} = 3^{-2 x+2}$

Since the powers of the same base are equal, we can set the exponents equal:

x+2 = -2x + 2

x+2 + 2x -2 = -2x + 2 + 2x -2

3x=0

x= 0

Now substitute in either function:

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

$f(0) = 3^{0 +2} = 3^{ 2} = 9$ , the correct answer.

Report an Error

Example Question #4 : Graphing

Define a function as follows:

$f(x) =5^{x-3}$

Give the -intercept of the graph of .

Possible Answers:

(0,15)

$\left ( 0, \frac{1}{125} \right )$

$\left ( 0,125 \right )$

$\left ( 0,243 \right )$

$\left ( 0, \frac{1}{243} \right )$

Correct answer:

$\left ( 0, \frac{1}{125} \right )$

Explanation:

Since the -intercept is the point at which the graph of intersects the -axis, the -coordinate is 0, and the -coordinate is f(0) :

$f(x) =5^{x-3}$

$f(0) =5^{0-3}= 5^{-3} = \frac{1}{5^{3}} = \frac{1}{125}$ ,

The -intercept is the point $\left ( 0, \frac{1}{125} \right )$ .

Report an Error

Example Question #6 : Graphing

$2 ^{x+1} + 3^{y} = 59$

$2 ^{x } - 3^{y} = -11$

Evaluate x+y .

Possible Answers:

The system has no solution.

Correct answer:

Explanation:

Rewrite the system as

$2 \cdot 2 ^{x} + 3^{y} = 59$

$2 ^{x } - 3^{y} = -11$

and substitute and for $2 ^{x }$ and $3^{y}$ , respectively, to form the system

2u + v= 59

u- v= -11

Add both sides:

2u + v= 5

$\underline{u- v= 43}$

=48

u = 16 .

Now backsolve:

16- v= -11

- v= - 27

v= 27

Now substitute back:

u = 16

$2 ^{x } = 16$

x = 4

and

v= 27

$3^{y}= 27$

y=3

x+y =4+3 = 7

Report an Error

Example Question #3 : Graphs Of Polynomial Functions

Give the -intercept of the graph of the function

$f(x) = 5 \cdot 4^{x- 3}- 3$

Round to the nearest tenth, if applicable.

Possible Answers:

(2.63,0)

(3.65,0)

( -3.08, 0)

( -2.92, 0)

The graph has no -interceptx

Correct answer:

(2.63,0)

Explanation:

The -intercept is (a,0) , where f(a)= 0 :

$f(x) = 5 \cdot 4^{x- 3}- 3$

$5 \cdot 4^{a- 3}- 3 = 0$

$5 \cdot 4^{a- 3}- 3 + 3= 0 + 3$

$5 \cdot 4^{a- 3}= 3$

$5 \cdot 4^{a- 3} \div 5= 3 \div 5$

$4^{a- 3} = 0.6$

$\ln \left (4^{a- 3} \right )=\ln 0.6$

$(a- 3)\ln 4 =\ln 0.6$

$a- 3=\frac{\ln 0.6}{\ln 4 } \approx \frac{-0.5108}{1.3863}\approx -0.3685$

$a- 3+3 \approx -0.3685 + 3$

$a \approx 2.63$

The -intercept is (2.63,0) .

Report an Error

Example Question #72 : Graphing

Give the -intercept of the graph of the function

$f(x) = 5 \cdot 4^{x- 3}- 3$

Round to the nearest hundredth, if applicable.

Possible Answers:

(0,3.65)

(0, -3.08)

( 0, 2.63)

The graph has no -intercept

(0, -2.92)

Correct answer:

(0, -2.92)

Explanation:

The -intercept is (0, f(0)) :

$f(x) = 5 \cdot 4^{x- 3}- 3$

$f(0) = 5 \cdot 4^{0- 3}- 3$

$f(0) = 5 \cdot 4^{ - 3}- 3$

$f(0) = 5 \cdot \frac{1}{64}- 3$

$f(0) = \frac{5}{64}- 3$

$f(0) \approx 0.08 - 3 \approx -2.92$

(0, -2.92) is the -intercept.

Report an Error

Example Question #72 : Graphing

Give the vertical asymptote of the graph of the function

$g(x) = 16 \cdot 4^{x}- 3$

Possible Answers:

y = -2

x = -3

The graph of has no vertical asymptote.

x = 3

y = 2

Correct answer:

The graph of has no vertical asymptote.

Explanation:

Since 4 can be raised to the power of any real number, the domain of is the set of all real numbers. Therefore, there is no vertical asymptote of the graph of .

Report an Error

View Tutors

Joshua
Certified Tutor

Murray State University, Bachelor in Arts, Spanish. Lipscomb University, Bachelor of Science, Teacher Assistant.

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

View Tutors

Lydia
Certified Tutor

The Richard Stockton College of New Jersey, Bachelor of Science, Biochemistry and Molecular Biology.

All Advanced Geometry Resources

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

Popular Subjects

Biology Tutors in San Diego, Math Tutors in Atlanta, Computer Science Tutors in Chicago, Computer Science Tutors in Atlanta, GMAT Tutors in Atlanta, Statistics Tutors in Atlanta, SAT Tutors in Phoenix, French Tutors in Seattle, SSAT Tutors in Washington DC, French Tutors in San Diego

Popular Courses & Classes

ISEE Courses & Classes in New York City, MCAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in New York City, GRE Courses & Classes in New York City, ISEE Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Philadelphia, GRE Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in San Diego, GRE Courses & Classes in Denver, SSAT Courses & Classes in Boston

Popular Test Prep

GRE Test Prep in San Diego, SAT Test Prep in Boston, MCAT Test Prep in Denver, SAT Test Prep in Seattle, GRE Test Prep in New York City, GRE Test Prep in Philadelphia, GRE Test Prep in Denver, ISEE Test Prep in Chicago, GMAT Test Prep in Chicago, GRE Test Prep in Los Angeles

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 : Graphing

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #141 : Coordinate Geometry

Example Question #3 : Graphing

Example Question #2 : Graphing

Example Question #4 : Graphing

Example Question #1 : How To Graph An Exponential Function

Example Question #4 : Graphing

Example Question #6 : Graphing

Example Question #3 : Graphs Of Polynomial Functions

Example Question #72 : Graphing

Example Question #72 : Graphing

All Advanced Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: