Graphing Rational Functions Part 2

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Presentation transcript:

Graphing Rational Functions Part 2 Precalculus 12.2

Ex. What is the end behavior for ? horizontal asymptote

What is the end behavior for ? Ex. What is the end behavior for ? slant asymptote notice that the difference in degree between numerator and denominator is 1

Ex. What is the end behavior for ? slant asymptote

What is the end behavior for ? Ex. What is the end behavior for ? parabolic asymptote notice that the difference in degree between numerator and denominator is 2

If the limit to infinity of a function: is a number goes to infinity with a degree difference of 1 goes to infinity with a degree difference of 2 horizontal asymptote slant asymptote parabolic asymptote

long division of polynomials How do we find the equation of the asymptote? long division of polynomials

Ex. Describe the end behavior and find the equation of the asymptote for . slant asymptote

Let’s put it all together…

Zeros Holes VA End Behavior Ex. For the given function, identify the zeros, holes, vertical asymptotes and end behavior. Sketch the graph and label. hole Zeros Holes VA End Behavior

End Behavior: Slant asymptote:

Zeros Holes VA End Behavior Ex. For the given function, identify the zeros, points of discontinuity by category and end behavior. Sketch the graph and label. Zeros Holes VA End Behavior

For your fun and enjoyment…