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Rational Functions: Slant Asymptotes

Rational Functions: Slant Asymptotes.

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Rational Functions: Slant Asymptotes

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  1. Rational Functions: Slant Asymptotes Slant Asymptotes: A Slant asymptote of a rational function is a slant line (equation: y = mx + b) such that as values of the independent variable, x, decrease without bound or increase without bound, the function values (y-values) approach (get closer and closer to) the y-values of the points on the slant asymptote (from either above or below). The next slide illustrates the definition.

  2. slant asymptote (dashed line) As x decreases the y-values of points on the graph get closer to the y-values of points on the asymptote. 4 3 2 1 As x increases the y-values of points on the graph get closer to the y-values of points on the asymptote. 0 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 Rational Functions: Slant Asymptotes Slide 2

  3. Example: Find the slant asymptote of - x slant asymptote y = x Rational Functions: Slant Asymptotes Divide the numerator by the denominator using the "long division" process. The slant asymptote is y = quotient. (This was the function shown graphed in the preceding slide!) Slide 3

  4. Try: Find the slant asymptote of Rational Functions: Slant Asymptotes The slant asymptote is y = 2x + 3. Slide 4

  5. Rational Functions: Slant Asymptotes END OF PRESENTATION Click to rerun the slideshow.

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