1. Objective: Students will be able to graph rational functions using their asymptotes and zeros.

2. Graphs of Rational Functions An asymptote of a function is a line that continuously approaches the function but never touches it at any point.

3. Determining Properties of Hyperbolas Identify the asymptotes, domain, and range of the following rational functions. Example 1: Asymptotes: Domain: Range:

4. Example 2: Asymptotes: Domain: Range:

5. Rational Function Properties Discontinuous function – a function whose graph has one or more gaps or breaks. (ex: hyperbola) Continuous function – a function whose graph has no gaps or breaks. (ex: linear, quadratic, polynomial)

6. Graphing Rational Functions with Vertical Asymptotes Directions: Identify the zeros and vertical asymptotes of the function. Then graph. Example 3: Zeros: Vertical Asymptote:

7. Example 4 Zeros: Vertical Asymptote:

9. Example 5 Directions: Identify the zeros and asymptotes of each function. Then graph using the graphing calculator. f(x) =

10. Example 6 f(x) =

11. Example 7 f(x) =

12. Homework for tonight Homework # _____ Textbook pg. 345 # 20, 21, 23, 25, 26, 27