Call Now to Set Up Tutoring:

(888) 888-0446

一个P Calculus BC : Functions, Graphs, and Limits

Study concepts, example questions & explanations for AP Calculus BC

Create An Account Create Tests & Flashcards

一个ll AP Calculus BC Resources

2 Diagnostic Tests 86 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 Next →

Example Question #1 :Identifying Asymptotes Graphically

一个symptoteplot

$\begin{align*}&\text{Decide which of the following functions, most likely represents the graph above.}\end{align*}$

Possible Answers:

$-\frac{(17x)}{(12x - 20)}$

$-\frac{(12x - 20)}{(17x)}$

$\frac{(12x - 20)}{(17x)}$

$\frac{(17x)}{(12x - 20)}$

Correct answer:

$\frac{(12x - 20)}{(17x)}$

Explanation:

$\begin{align*}&\text{Notice that as x increases, the function graphed appears to}\\&\text{level out, flattening towards a certain value. This value is}\\&\text{what is known as a horizontal asymptote. An asymptote is a value}\\&\text{that a function approaches, but never actually reaches. Think}\\&\text{of a horizontal asymptote as the limit of a function as x approaches}\\&\text{infinity. In such a case, as x approaches infinity, any constants}\\&\text{added or subtracted in the numerator and denominator become}\\&\text{irrelevant. What matters is the power of x in the denominator}\\&\text{and the numerator; if those are the same, then the coefficients}\\&\text{define the asymptote. We see that the function flattens towards:}\\&f(\infty)=0.71\\&\text{This matches the ratio of coefficients for the function: }\\&\frac{(12x - 20)}{(17x)}\end{align*}$

Report an Error

Example Question #2 :Identifying Asymptotes Graphically

一个symptoteplot

$\begin{align*}&\text{Decide which of the following functions, most likely represents the graph above.}\end{align*}$

Possible Answers:

$\frac{(16x - 13)}{(9x - 4)}$

$-\frac{(9x - 4)}{(16x - 13)}$

$-\frac{(16x - 13)}{(9x - 4)}$

$\frac{(9x - 4)}{(16x - 13)}$

Correct answer:

$\frac{(16x - 13)}{(9x - 4)}$

Explanation:

$\begin{align*}&\text{Notice that as x increases, the function graphed appears to}\\&\text{level out, flattening towards a certain value. This value is}\\&\text{what is known as a horizontal asymptote. An asymptote is a value}\\&\text{that a function approaches, but never actually reaches. Think}\\&\text{of a horizontal asymptote as the limit of a function as x approaches}\\&\text{infinity. In such a case, as x approaches infinity, any constants}\\&\text{added or subtracted in the numerator and denominator become}\\&\text{irrelevant. What matters is the power of x in the denominator}\\&\text{and the numerator; if those are the same, then the coefficients}\\&\text{define the asymptote. We see that the function flattens towards:}\\&f(\infty)=1.78\\&\text{This matches the ratio of coefficients for the function: }\\&\frac{(16x - 13)}{(9x - 4)}\end{align*}$

Report an Error

Example Question #3 :Identifying Asymptotes Graphically

一个symptoteplot

$\begin{align*}&\text{Of the following functions, which most likely represents the graph above?}\end{align*}$

Possible Answers:

$\frac{(15x - 16)}{(3x + 14)}$

$-\frac{(15x - 16)}{(3x + 14)}$

$\frac{(3x + 14)}{(15x - 16)}$

$-\frac{(3x + 14)}{(15x - 16)}$

Correct answer:

$\frac{(3x + 14)}{(15x - 16)}$

Explanation:

$\begin{align*}&\text{Notice that as x increases, the function graphed appears to}\\&\text{level out, flattening towards a certain value. This value is}\\&\text{what is known as a horizontal asymptote. An asymptote is a value}\\&\text{that a function approaches, but never actually reaches. Think}\\&\text{of a horizontal asymptote as the limit of a function as x approaches}\\&\text{infinity. In such a case, as x approaches infinity, any constants}\\&\text{added or subtracted in the numerator and denominator become}\\&\text{irrelevant. What matters is the power of x in the denominator}\\&\text{and the numerator; if those are the same, then the coefficients}\\&\text{define the asymptote. We see that the function flattens towards:}\\&f(\infty)=0.2\\&\text{This matches the ratio of coefficients for the function: }\\&\frac{(3x + 14)}{(15x - 16)}\end{align*}$

Report an Error

Example Question #11 :渐近和无限的行为

一个symptoteplot

$\begin{align*}&\text{Decide which of the following functions, most likely represents the graph above.}\end{align*}$

Possible Answers:

$\frac{(12x - 10)}{(20x + 10)}$

$\frac{(20x + 10)}{(12x - 10)}$

$-\frac{(20x + 10)}{(12x - 10)}$

$-\frac{(12x - 10)}{(20x + 10)}$

Correct answer:

$-\frac{(20x + 10)}{(12x - 10)}$

Explanation:

$\begin{align*}&\text{Notice that as x increases, the function graphed appears to}\\&\text{level out, flattening towards a certain value. This value is}\\&\text{what is known as a horizontal asymptote. An asymptote is a value}\\&\text{that a function approaches, but never actually reaches. Think}\\&\text{of a horizontal asymptote as the limit of a function as x approaches}\\&\text{infinity. In such a case, as x approaches infinity, any constants}\\&\text{added or subtracted in the numerator and denominator become}\\&\text{irrelevant. What matters is the power of x in the denominator}\\&\text{and the numerator; if those are the same, then the coefficients}\\&\text{define the asymptote. We see that the function flattens towards:}\\&f(\infty)=-1.67\\&\text{This matches the ratio of coefficients for the function: }\\&-\frac{(20x + 10)}{(12x - 10)}\end{align*}$

Report an Error

Example Question #12 :渐近和无限的行为

一个symptoteplot

$\begin{align*}&\text{Decide which of the following functions, most likely represents the graph above.}\end{align*}$

Possible Answers:

$-\frac{(3x + 18)}{(16x - 9)}$

$-\frac{(6x - 18)}{(16x + 9)}$

$-\frac{(16x - 9)}{(3x + 18)}$

$-\frac{(16x + 9)}{(6x - 18)}$

Correct answer:

$-\frac{(6x - 18)}{(16x + 9)}$

Explanation:

$\begin{align*}&\text{Notice that as x increases, the function graphed appears to}\\&\text{level out, flattening towards a certain value. This value is}\\&\text{what is known as a horizontal asymptote. An asymptote is a value}\\&\text{that a function approaches, but never actually reaches. Think}\\&\text{of a horizontal asymptote as the limit of a function as x approaches}\\&\text{infinity. In such a case, as x approaches infinity, any constants}\\&\text{added or subtracted in the numerator and denominator become}\\&\text{irrelevant. What matters is the power of x in the denominator}\\&\text{and the numerator; if those are the same, then the coefficients}\\&\text{define the asymptote. We see that the function flattens towards:}\\&f(\infty)=-\frac{3}{8}\\&\text{This matches the ratio of coefficients for the function: }\\&-\frac{(6x - 18)}{(16x + 9)}\end{align*}$

Report an Error

← Previous 1 2 3 4 5 6 7 8 Next →

View AP Calculus BC Tutors

Brandon
Certified Tutor

University of Wyoming, Bachelor of Science, Physics. University of Wyoming, Bachelor of Science, Mathematics.

View AP Calculus BC Tutors

Nicole
Certified Tutor

College of St Benedict, Bachelor in Arts, Economics. University of South Florida-Main Campus, Master of Arts, Economics.

View AP Calculus BC Tutors

Margaret
Certified Tutor

Case Western Reserve University, Bachelor of Science, Statistics. Case Western Reserve University, Master of Science, Economi...

一个ll AP Calculus BC Resources

2 Diagnostic Tests 86 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Dallas Fort Worth,GMAT Tutors in Houston,Computer Science Tutors in Boston,ISEE Tutors in New York City,GMAT Tutors in Washington DC,SAT Tutors in Miami,Statistics Tutors in Phoenix,Calculus Tutors in Los Angeles,English Tutors in Boston,Statistics Tutors in Los Angeles

Popular Courses & Classes

Spanish Courses & Classes in Houston,SAT Courses & Classes in San Francisco-Bay Area,MCAT Courses & Classes in Seattle,ISEE Courses & Classes in Boston,GMAT Courses & Classes in San Diego,MCAT Courses & Classes in New York City,LSAT Courses & Classes in Boston,MCAT Courses & Classes in Los Angeles,一个CT Courses & Classes in Seattle,LSAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

ISEE Test Prep in Seattle,GRE Test Prep in Seattle,GMAT Test Prep in Phoenix,SSAT Test Prep in Philadelphia,SAT Test Prep in Washington DC,一个CT Test Prep in Boston,MCAT Test Prep in New York City,ISEE Test Prep in Atlanta,一个CT Test Prep in Seattle,GMAT Test Prep in San Francisco-Bay Area

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:

copyrigh的物理或电子签名t 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

一个ddress

*一个ddress1

一个ddress2

*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

科学辅导

foreign languages

elementary tutoring

other

Search 350+ Subjects

一个P Calculus BC : Functions, Graphs, and Limits

Study concepts, example questions & explanations for AP Calculus BC

一个ll AP Calculus BC Resources

Example Questions

Example Question #1 :Identifying Asymptotes Graphically

Example Question #2 :Identifying Asymptotes Graphically

Example Question #3 :Identifying Asymptotes Graphically

Example Question #11 :渐近和无限的行为

Example Question #12 :渐近和无限的行为

一个ll AP Calculus BC Resources

Report an issue with this question

DMCA Complaint

Contact Information

一个ddress

Complaint Details

Find the Best Tutors

Email address:
Your name:
Feedback: