1. Table of Contents 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. Table of Contents Rational Functions: Slant Asymptotes Slide 2 -4 -3 -2 0 1 2 3 4 -4-3-21234 slant asymptote (dashed line) As x increases the y-values of points on the graph get closer to the y-values of points on the asymptote. As x decreases the y-values of points on the graph get closer to the y-values of points on the asymptote.

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

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

5. Table of Contents Rational Functions: Slant Asymptotes