Properties of Rational Functions Characteristics of the Graph

Properties of Rational Functions Characteristics of the Graph of a Rational Function: Let

Properties of Rational Functions End Behavior Asymptote (Horizontal/Oblique): If n<m the EBA is y=0 We will use limits to describe!!! If n=m the EBA is If n>m the EBA is Where with the remainder being ignored. How do we divide functions? ? ?

Properties of Rational Functions vertical asymptote: Occurs at unique zeros of the denominator (not zeros of the numerator) (set the den=0 and solve) *we will use limits to describe x-intercepts: Occurs at the zeros of the numerator that are also not zeros of the denominator. (set num=0 and solve) y-intercepts: The value of f(0) if defined. (substitute 0 into function and solve)

Example 1: Find the asymptotes and intercepts of the function Since n>m our EBA = q(x) What kind of EBA is it? (Hint: Graph and look) How was q(x) found? ? ?

Ex 1: Find the asymptotes and intercepts of the function Factoring the denominator for vertical asymptotes:

Ex 1: Find the asymptotes and intercepts of the function Setting the numerator equal to 0 for xintercepts:

Ex 1: Find the asymptotes and intercepts of the function Finding f(0) for y-intercepts:

Let’s Talk About Limits!!! Pg. 225: #s 25, 27, 29

4. 4 HW Assignment Pg. 225 #s 14 -30 evens, 44 -50 evens, 60 (use limits to describe all vertical and horizontal asymptotes on 44 -50 evens ONLY)