Presentation on theme: "Homework Check – have homework ready! Learning Goals: Find the Domain of a Rational Function Find the equation of the Vertical and Horizontal Asymptotes."— Presentation transcript:
Homework Check – have homework ready! Learning Goals: Find the Domain of a Rational Function Find the equation of the Vertical and Horizontal Asymptotes (if they exist) Sketch the graph of a Rational Function
A Rational Function is the quotient of two polynomial functions. The domain of a rational function is all Real numbers, excluding numbers that make the denominator zero.
An Asymptote is a line that a function approaches but does not cross. ◦ Vertical Asymptotes are Vertical lines that occur at the places where the denominator = zero, (except for common factors in the numerator.) x approaches some value c, f(x) approaches ∞
Horizontal Asymptotes are horizontal lines that a rational function approaches at the ends. Consider the rational function: If n < m, then the Horz. Asym. is y = 0. If n = m, then the Horz. Asym. is If n > m, then there is no Horz. Asym. x approaches ±∞, f(x) approaches some value c
Find the Domain of the Function, and the Vertical and Horizontal Asymptotes. Pg. 138, #1. Domain: solve Domain: All Real Numbers, Vertical Asymptotes - Horizontal Asymptotes Look at the End Behavior What happens when x gets big?
1.1. Find Zeros of the Numerator Graph bounces or crosses 2.2. Find Zeros of the Denominator Vertical Asymptotes 3.3. Determine End Behavior Horizontal Asymptotes 4.4. Test Intervals Is the graph neg. or pos. 5.5. Find specific key points Graphical Precision