Warm-up Check skills p 491 (1 – 9)

Section 9-3: Rational Functions and Their Graphs Goal 2.05: Use rational equations to solve problems. B) Interpret the constants and coefficients in the context of the problem. C) Identify the asymptotes and intercepts graphically and algebraically.

Vertical Asymptotes Copy Vertical Asymptotes Properties from page 493. Ex:

Example y= (x + 2) (x + 2)(x – 2) There would be a hole at x = -2, and a vertical asymptote at x = 2.

Horizontal: Rational functions have at most one horizontal asymptote. y= 0 if the degree of the denominator is greater than the degree of the numerator. ex: 1/(x + 2)

Example y= a/b if the degree of the denominator equals the degree of the numerator where a is the coefficient of the term with highest degree in the numerator and b is the coefficient of the term with highest degree in the denominator. ex: x/ (x – 1 ) Horizontal asymptote at 1/1 or 1

If the degree of the numerator is greater than the degree of the denominator, then the graph does not have a horizontal asymptote. ex: y= ( x )/ (x + 5 )

Describe Vertical Asymptotes/Holes

Classwork P 485 #2 – 30 even