Call Now to Set Up Tutoring:

(917) 215-4373

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Want to review Common Core: High School - Functions but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different Common Core: High School - Functions flashcards! Our Common Core: High School - Functions flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous Common Core: High School - Functions flashcards.

Flashcards: Graph Rational Functions, Identify Zeros, Asymptotes, and End Behavior: CCSS.Math.Content.HSF-IF.C.7d

Graph the following function and its asymptotes.

$f(x)=\frac{1}{x+3}$

Screen shot 2016 01 13 at 12.43.56 pm

$\textup{Asymptotes: }x=-3, y=0$

Screen shot 2016 01 13 at 12.43.56 pm

$\textup{Asymptote: }x=-3$

Screen shot 2016 01 13 at 12.58.06 pm

$\textup{Asymptote: }x=3$

Screen shot 2016 01 13 at 12.58.06 pm

$\textup{Asymptotes: }x=3, y=0$

Screen shot 2016 01 13 at 1.00.17 pm

$\textup{Asymptote: } y=0$

Report an Error Copyright Notice

Flashcards: Graph Rational Functions, Identify Zeros, Asymptotes, and End Behavior: CCSS.Math.Content.HSF-IF.C.7d

Graph the following function and its asymptotes.

$f(x)=\frac{1}{x+3}$

Your answer:

Screen shot 2016 01 13 at 12.43.56 pm

$\textup{Asymptote: }x=-3$

Your answer:

Screen shot 2016 01 13 at 12.58.06 pm

$\textup{Asymptote: }x=3$

Your answer:

Screen shot 2016 01 13 at 12.58.06 pm

$\textup{Asymptotes: }x=3, y=0$

Your answer:

Screen shot 2016 01 13 at 1.00.17 pm

$\textup{Asymptote: } y=0$

Correct answer:

Screen shot 2016 01 13 at 12.43.56 pm

$\textup{Asymptotes: }x=-3, y=0$

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic techniques to identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

$y=\frac{1}{a-x} \rightarrow a-x\neq 0\rightarrow a\neq x$

Given the function

$f(x)=\frac{1}{x+3}$

$\\x+3\neq0 \\x\neq-3$

thus a vertical asymptote is at x=-3 .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

$f(x)=\frac{1}{x+3}$

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger.

Recall that when n is some large value, the fraction approaches zero.

$\frac{1}{n}\rightarrow 0$

Therefore, the horizontal asymptote is at y=0 .

Step 3: Graph the function using technology and plot the asymptotes.

Screen shot 2016 01 13 at 12.43.56 pm

Flashcards: Graph Rational Functions, Identify Zeros, Asymptotes, and End Behavior: CCSS.Math.Content.HSF-IF.C.7d

Graph the function and its asymptotes.

$f(x)=\frac{1}{x}$

Screen shot 2016 01 13 at 12.58.06 pm

$\text{Asymptotes: }x=0$

Screen shot 2016 01 13 at 12.58.06 pm

$\text{Asymptotes: }x=0, y=0$

Screen shot 2016 01 13 at 12.43.56 pm

$\text{Asymptotes: }x=-3$

Screen shot 2016 01 13 at 12.43.56 pm

$\text{Asymptotes: }x=0, y=0$

Question2

$\text{Asymptotes: }x=0, y=0$

Report an Error Copyright Notice

Flashcards: Graph Rational Functions, Identify Zeros, Asymptotes, and End Behavior: CCSS.Math.Content.HSF-IF.C.7d

Graph the function and its asymptotes.

$f(x)=\frac{1}{x}$

Your answer:

Screen shot 2016 01 13 at 12.58.06 pm

$\text{Asymptotes: }x=0$

Your answer:

Screen shot 2016 01 13 at 12.58.06 pm

$\text{Asymptotes: }x=0, y=0$

Your answer:

Screen shot 2016 01 13 at 12.43.56 pm

$\text{Asymptotes: }x=-3$

Your answer:

Screen shot 2016 01 13 at 12.43.56 pm

$\text{Asymptotes: }x=0, y=0$

Correct answer:

Question2

$\text{Asymptotes: }x=0, y=0$

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic techniques to identify asymptotes of the function.

$y=\frac{1}{a-x} \rightarrow a-x\neq 0\rightarrow a\neq x$

Given the function

$f(x)=\frac{1}{x}$

$x\neq0$

thus a vertical asymptote is at x=0 .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

$f(x)=\frac{1}{x}$

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger.

Recall that when n is some large value, the fraction approaches zero.

$\frac{1}{n}\rightarrow 0$

Therefore, the horizontal asymptote is at y=0 .

Step 3: Graph the function using technology and plot the asymptotes.

Question2

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)

View Tutors

Rachel
Certified Tutor

Henderson State University, Bachelor of Science, Biology, General.

View Tutors

Caroline
Certified Tutor

Liberty University, Master of Arts, Counselor Education.

View Tutors

Mrudul
Certified Tutor

University of Pittsburgh, Bachelor's, Neuroscience.

Popular Subjects

LSAT Tutors in Los Angeles, Math Tutors in Phoenix, LSAT Tutors in Houston, Physics Tutors in New York City, Reading Tutors in Miami, MCAT Tutors in Boston, Statistics Tutors in San Francisco-Bay Area, ISEE Tutors in Phoenix, Computer Science Tutors in Washington DC, Computer Science Tutors in Atlanta

Popular Courses & Classes

LSAT Courses & Classes in Washington DC, MCAT Courses & Classes in San Diego, ISEE Courses & Classes in Seattle, ACT Courses & Classes in Washington DC, MCAT Courses & Classes in Miami, Spanish Courses & Classes in Denver, ISEE Courses & Classes in Chicago, SSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Seattle, MCAT Courses & Classes in New York City

Popular Test Prep

SSAT Test Prep in San Diego, GRE Test Prep in Miami, GRE Test Prep in Los Angeles, GRE Test Prep in Atlanta, GMAT Test Prep in Atlanta, GRE Test Prep in San Francisco-Bay Area, SSAT Test Prep in Atlanta, MCAT Test Prep in San Diego, ISEE Test Prep in Chicago, ACT Test Prep in New York City

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

All Common Core: High School - Functions Resources

Flashcards: Graph Rational Functions, Identify Zeros, Asymptotes, and End Behavior: CCSS.Math.Content.HSF-IF.C.7d

Flashcards: Graph Rational Functions, Identify Zeros, Asymptotes, and End Behavior: CCSS.Math.Content.HSF-IF.C.7d

Flashcards: Graph Rational Functions, Identify Zeros, Asymptotes, and End Behavior: CCSS.Math.Content.HSF-IF.C.7d

Flashcards: Graph Rational Functions, Identify Zeros, Asymptotes, and End Behavior: CCSS.Math.Content.HSF-IF.C.7d

Report an issue with this question