1. Warm-Up

2. Unit 2.5: Rational Functions

4. 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 -∞

5. 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!

7. 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 -∞

10. Rules for graphs of rational functions

11. 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.

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

13. Graphing rational functions

14. Graphing rational functions

15. Practice…

16. Graphing rational functions

17. Practice makes perfect!