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Lesson 2.6 Rational Functions and Asymptotes

Lesson 2.6 Rational Functions and Asymptotes. Graph the function: Domain: Range: Increasing/Decreasing: Line that creates a split in the graph:. Rational Functions Where N(x) and D(x) are polynomials Discontinuities: places where the graph “skips” or “jumps”

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Lesson 2.6 Rational Functions and Asymptotes

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  1. Lesson 2.6Rational Functions andAsymptotes

  2. Graph the function: Domain: Range: Increasing/Decreasing: Line that creates a split in the graph:

  3. Rational Functions Where N(x) and D(x) are polynomials Discontinuities: places where the graph “skips” or “jumps” Graph and look for discontinuities:

  4. Discontinuities Hole: can be factored out Jumps: cannot be factored out Asymptotes (jumps) A horizontal or vertical line through which a graph is undefined Cannot be factored out

  5. Finding location of asymptotes: Given ; n = degree of N(x), d = degree of D(x) Vertical asymptote(s): At zeros of D(x); Write “x = #” Horizontal asymptote(s): If n < d→ → y = 0 If n = d → → If n > d → → no horizontal asymptote

  6. Example Find all discontinuities of Problem Set 2.6

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