 # Homework Check – have homework ready! Learning Goals: Find the Domain of a Rational Function Find the equation of the Vertical and Horizontal Asymptotes.

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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

1.4. 2.5. 3.6.

 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

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