1. Advanced Precalculus Notes 3.3 Properties of Rational Functions Rational function: given: q(x) is not the zero polynomial

2. Specify the Domain of each function: a) b) c) d) e)

3. Vertical asymptotes: x values that make the denominator zero. Horizontal asymptotes: value which the function approaches as x approaches. x-intercept: set the numerator equal to zero. y-intercept: substitute 0 for x.

4. Analyze: X-intercept __________x-intercept _________ Y-intercept__________y-intercept_________ Vertical Asymptotes__________Asymptotes_________ Horizontal Asymptotes__________Asymptotes__________

5. XYXYXYXY 10-101.52.1 100-1001.92.01 1000-10001.992.001 10000-100001.9992.0001 Complete each table for g(x)

6. An asymptote is like one of those people you meet at a party who is devastatingly attractive and you just want to get close. You maneuver your way next to them and casually strike up a conversation. Making good time, you get closer and closer, till you're practically knocking knees. In calculus, you just keep getting closer. Horizontal asymptote: As x → - or as x →, if the function value approaches a fixed number L, then the line y = L is a horizontal asymptote. Graph MAY intersect. Vertical asymptote: For each function, find the x-intercepts (if they exist), y-intercepts (if they exist), vertical asymptotes (if they exist), horizontal asymptotes (if they exist). Graph CANNOT intersect. Oblique asymptote: A slant asymptote which shows end result.

7. 1) 2) x-intercept ________ y-intercept ________ vertical asymptote(s) _________ vertical asymptote(s) __________ horizontal asymptote(s) ________ Graph

8. 3)4) x-intercept ________ y-intercept ________ vertical asymptote(s) _________ vertical asymptote(s) __________ horizontal asymptote(s) ________ Graph

9. 5)6) x-intercept ________ y-intercept ________ vertical asymptote(s) _________ vertical asymptote(s) __________ horizontal asymptote(s) ________ Graph

10. Oblique Asymptotes: Find the horizontal or oblique asymptotes, if any:

11. Assignment: page 195: 1 – 10, 13, 18, 23, 25, 26, 31, 37, 39, 41, 45, 46, 47, 51