Rational functions are quotients of polynomial functions.

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Presentation transcript:

Rational functions are quotients of polynomial functions. Objective: Find asymptotes of rational functions and behavior around asymptotes. Rational functions are quotients of polynomial functions.

Example 1 Find the domain of each rational function. a. b. c.

Vertical Asymptotes: zeros of the denominator Vertical Asymptotes: zeros of the denominator. (If there are no common factors for numerator and denominator) Horizontal Asymptotes: Leading terms If n = m; If m > n; If m < n; no H.A. Oblique Asymptotes: when m < n; divide numerator by denominator.

Example 2 Find the vertical asymptotes. a. b. c.

Example 3 Find the horizontal asymptotes. a. b. c.

Example 4 Find the horizontal and vertical asymptotes. a. b.

Example 5 Describe the end behavior and the behavior around the vertical asymptote. a.

b.

Assignment: pg 354 #1-36