1. 1 What you will learn 1. How to graph a rational function based on the parent graph. 2. How to find the horizontal, vertical and slant asymptotes for a rational function.

2. Objective: Section 3-7 Graphs of Rational Functions 2 Yeah! Definitions 1. Rational Function: A quotient of two polynomial functions. 2. Asymptote: A line that a graph approaches but never intersects. (Can be horizontal, vertical, or slant)

3. Objective: Section 3-7 Graphs of Rational Functions 3 Types of Asymptotes  Horizontal asymptote: the line y = b is a horizontal asymptote for a function f(x) if f(x) approaches b as x approaches infinity or as x approaches negative infinity.  Vertical asymptote: the line x = a is a vertical asymptote for a function f(x) if f(x) approaches infinity or f(x) approaches negative infinity as x approaches “a” from either the left or the right.  Slant asymptote: the oblique line “l” is a slant asymptote for a function f(x) if the graph of y = f(x) approaches “l” as x approaches infinity or as x approaches negative infinity.

4. Objective: Section 3-7 Graphs of Rational Functions 4 Visual Vocabulary Vertical asymptote Horizontal Asymptote

5. Objective: Section 3-7 Graphs of Rational Functions 5 Slant Asymptote

6. Objective: Section 3-7 Graphs of Rational Functions 6 Finding Asymptotes Find the asymptotes for the graph of Vertical asymptote: value of x that causes a “0” in the denominator.x – 2 = 0 x = 2 is vert. as. Check: XF(x) 1.9 1.99 1.999 1.9999

7. Objective: Section 3-7 Graphs of Rational Functions 7 Finding Asymptotes (cont.) Find the asymptotes for the graph of Horizontal asymptotes: Divide the numerator and the denominator by the highest power of x. Ask yourself, as x gets infinitely large, what would the value of the function be?

8. Objective: Section 3-7 Graphs of Rational Functions 8 You Try Determine the asymptotes for the graph of:

9. Objective: Section 3-7 Graphs of Rational Functions 9 Finding Slant Asymptotes  Slant asymptotes occur when the degree of the numerator of a rational function is exactly one greater than the degree of the denominator.  Example: Find the slant asymptote for:

10. Objective: Section 3-7 Graphs of Rational Functions 10 You Try  Find the slant asymptote for:

11. Objective: Section 3-7 Graphs of Rational Functions 11 Graphing Rational Functions  Can you predict what will happen as we graph the following: 1.2. 3.4.

12. Objective: Section 3-7 Graphs of Rational Functions 12 Let’s See

13. Objective: Section 3-7 Graphs of Rational Functions 13 How About…

14. Objective: Section 3-7 Graphs of Rational Functions 14 How About…

15. Objective: Section 3-7 Graphs of Rational Functions 15 How About

16. Objective: Section 3-7 Graphs of Rational Functions 16 You Try!  How will the following functions relate to the parent graph?

17. Objective: Section 3-7 Graphs of Rational Functions 17 A Last Note…  Graph

18. Objective: Section 3-7 Graphs of Rational Functions 18 Homework  Page 186, 14, 16, 18, 22, 24, 26, 30, 32, 36