Rational Functions Slant Asymptotes A Slant asymptote of

Rational Functions: 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. Table of Contents

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

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

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

Rational Functions: Slant Asymptotes Table of Contents