1. Introducing Oblique Asymptotes Horizontal Asymptote Rules: – If numerator and denominator have equal highest power, simplified fraction is the H.A. – If denominator has a higher power than the numerator the H.A. is zero – What happens when the numerator has a higher power than the denominator?

2. Rational Functions – Oblique Asymptotes Oblique Asymptotes – Sometimes called slant asymptotes Happens when the degree of the numerator is greater than the degree of the denominator.

3. Rational Functions – Oblique Asymptotes How to Graph a Rational Function that Contains an Oblique Asymptote 1.Find Vertical Asymptote Normal Way (set denominator = to zero) 2.Find roots the normal way (set entire function = to zero) 3.Find oblique asymptote Divide numerator by denominator by either polynomial or synthetic division Resulting quotient is oblique asymptote (ignore remainder. 4.Test zones as you normally would (are points above or below oblique asymptote?)

4. Rational Functions – Oblique Asymptotes Examples: 1.f(x) = x 2 – x – 2 x – 1 2.f(x) = x 2 – x x + 1