• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
Rational functions

Rational functions



Rational functions for Pre-cal

Rational functions for Pre-cal



Total Views
Views on SlideShare
Embed Views



2 Embeds 3

http://precalculus-mann.wikispaces.com 2
http://learn.idahodigitallearning.org 1



Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
Post Comment
Edit your comment

    Rational functions Rational functions Presentation Transcript

    • Rational Functions
      By: Katie Thayer
    • A rational function is any function which can be written as the ratio of two polynomial functions.
      What is a Rational Function?
    • Asymptotes
      Asymptote - a straight line that is the limiting value of a curve
      The red line on the graph indicates that y=x is the asymptote.
    • 2 types
      There are two types of asymptotes.
      Vertical Asymptote- x=___, ** CAN’T BE CROSSED**. Can be found be the zeros, or x- intercepts, which are in the denominator.
      Horizontal Asymptote- y=___, ** Can be crossed*. But there are three different ways you can find a horizontal asymptote.
    • VA and HA
      The Vertical Asymptote of out function would be, x=-3 and x=1
      The Horizontal Asymptote is y=0.
    • Three types of Horizontal asymptote.
      Type 1: when the degree of the denominator- degree being the exponential value of x- is larger than the degree of the numerator, then the HA is y=0.
      Type 2: When the numerator degree and the denominator degree are the same , y=
      The HA= y=
      * When the power of the numerator is bigger than the denominator, the asymptote with be a slant, or oblique. To find the horizontal asymptote of these equations you have to use long division.
    • X-intercepts.
      To find the x- intercepts you have to take the numerator and set it equal to zero. Going back to the first equation this is what find the x-ints, would look like. The you solve for x by dividing both sides by -5 . So you would get, and since zero can’t be divided , There are no x- intercepts.
    • Y- intercepts.
      To find the y- intercepts you set x = to zero. And it equals 0, so the y- intercept would be at the origin, (0,0).
    • tables
      To find possible points of where the line would cross on a graph, you make an x-y tables, of x’s to the left and right of each asymptote.
    • Domain and Range
      The domain of a function is the set of all possible x values which will make the function "work" and will output real y-values
      The range of a function is the possible y values of a function that result when we substitute all the possible x-values into the function.
    • The domain in the graph is (-∞,o)U (0,∞)The range would be the same.
    • Domain and Range cont.
      The Domain of this function would be
      D: (-∞,-3] U [-3,1] U [1,∞)
      The Range would be (-∞,∞)