Rational Functions Objectives: Graph rational functions.

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Presentation transcript:

Rational Functions Objectives: Graph rational functions. Determine vertical, horizontal, and slant asymptotes. JReasons Saturday, February 16, 2019

JReasons Saturday, February 16, 2019

JReasons Saturday, February 16, 2019

JReasons Saturday, February 16, 2019

y y = R(x) y = L x y y = L x y = R(x) JReasons Saturday, February 16, 2019

JReasons Saturday, February 16, 2019

x = c y x x = c y x JReasons Saturday, February 16, 2019

If an asymptote is neither horizontal nor vertical it is called oblique (slant). x JReasons Saturday, February 16, 2019

JReasons Saturday, February 16, 2019

JReasons Saturday, February 16, 2019

Theorem Locating Vertical Asymptotes JReasons Saturday, February 16, 2019

JReasons Saturday, February 16, 2019

Vertical asymptotes: x = -1 and x = 1 No vertical asymptotes Vertical asymptote: x = -4 JReasons Saturday, February 16, 2019

1. If n < m, then y = 0 is a horizontal asymptote of the graph of R. 2. If n = m, then y = an / bm is a horizontal asymptote of the graph of R. 3. If n = m + 1, then y = ax + b is an oblique asymptote of the graph of R. Found using long division. 4. If n > m + 1, the graph of R has neither a horizontal nor oblique asymptote. JReasons Saturday, February 16, 2019

JReasons Saturday, February 16, 2019

Horizontal asymptote: y = 0 JReasons Saturday, February 16, 2019

Oblique asymptote: y = x + 6 JReasons Saturday, February 16, 2019