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Presentation transcript:

Warm-Up

Unit 2.5: Rational Functions

The simplest of all rational functions: Recall the end behavior for this function: The line y = c is considered to be a horizontal asymptote if c is the limit as x approaches ∞ and -∞

How is this related to the function itself? Notice how the y-values go towards ±∞ when x = 0. This line is known as a vertical asymptote. How is this related to the function itself? It is a zero of the denominator. It is not a zero of the numerator. This means you can graph these without at calculator!

Finding the asymptotes Check for vertical asymptotes. Need to determine whether x=3 is a point of infinite discontinuity. Find the limit as x approaches 3 from the left and the right Check for horizontal asymptotes. Use a table to examine the end behavior or, fill in ∞ and -∞

Rules for graphs of rational functions

To graph a rational function: Find the domain. Find and sketch the asymptotes (vertical and horizontal), if any. Find and plot the x-intercepts and y-intercept, if any. Find and plot at least one point in the test intervals determined by any x-intercepts and vertical asymptotes.

Review: to find the x and y intercepts… An x-intercept is: For a rational function, what does this mean? A y-intercept is:

Graphing rational functions

Graphing rational functions

Practice…

Graphing rational functions

Practice makes perfect!