ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

How to Graph a Rational Function

Updated on April 30, 2013

Rational Functions!

A rational function graphed
A rational function graphed | Source

What is a Rational Function?

Rational - A rational number is a number that can be written as a fraction, repeating, or terminating decimal.


A function is a relationship between an x value and y value. The input and output values of a function relate to one another.

A function must work for every input value. It also must have only one y value for every x value.

Remember the vertical line test. For every x there must only be one y value or it is not a function.

A Rational Function is a function that is written as a ratio or division of polynomial functions.

Polynomial functions are functions that contain more than one term. Poly refers to many. Bi refers to two.

Basic Rational Function

This function has an asymptote at y= 0 and x = 0
This function has an asymptote at y= 0 and x = 0 | Source

Graph the Function

the function
the function | Source
the intercepts
the intercepts | Source
the points
the points | Source
Connect the dots
Connect the dots | Source

Graphing the Function - Asymptotes

The first thing you look for when graphing a rational function is the asymptote of the function.

The vertical asymptote is when y approach f(x) x approach + or - infinity.

The horizontal asymptote is an imaginary line where the

Finding the Intercepts

The next step is to figure out where the function passes through the x and y axis. These are referred to as the intercepts.

You are looking for the value of x when y =0 and the y value when x=0. Find the value and put the in coordinate point form.

Plot these points on the graph.

Plot a Few Points

Plot several points close to key features of the function in order to sketch out what the functions looks like. I like to plot points that will start to show the shape of the function.

In the example I plotted several points so that I can begin to see the shape which this function creates.

Connect the Dots

Connect your rough sketches of your points and extend the lines onward to create a graph of a radical function.

The example shows a curved radical function. Notice that connecting the dots is more fluid than when you were in kindergarten.

Using Tools to Graph

Online graphing tools can help easily and effectively graph these lines. These tools are free and easy to use. They preform similar functions as a graphing calculator but are easier to read and manipulate the data as needed.

Quiz Time



Think about the radical function, both the graph and the function are shown.

See if you can identify the key elements of the radical function.

Use Your Knowledge Base

Use what you already know about functions, graphing, and polynomials to help you graph rational functions. Remember these are rational numbers so there will not be answers that include complex or imaginary roots.

Use your graphing calculator and tools to help you find the information you need to graph the function.

Use online tools to create a graph that you can print out and attach to your homework if necessary, make sure your teacher allows this first. They may require to see your input and work that went along with your print out if this is excepted.


    0 of 8192 characters used
    Post Comment

    No comments yet.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)