3.5 Rational Functions II: Analyzing Graphs

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Presentation transcript:

3.5 Rational Functions II: Analyzing Graphs

Analyzing the Graph of a Rational Function Find the domain of the rational function R. Write R in the lowest terms. Locate the x and y intercepts. Test for symmetry. Locate vertical asymptotes. Locate horizontal and oblique asymptotes. Graph R.

Analyze the graph of:

In lowest terms: x-intercept: -1 y-intercept: No symmetry

Vertical asymptote: x = -3 Hole: (3, 4/3) Horizontal asymptote: y = 2

1 -4 -2 R(1) = 1 R(-4) = 6 R(-2) = -2 Above x-axis Above x-axis Below x-axis (-4, 6) (-2, -2) (1, 1)

x = - 3 (-4, 6) (1, 1) (3, 4/3) y = 2 (-2, -2) (-1, 0) (0, 2/3)