5.3.lesson.part2

# 5.3.lesson.part2 - 5.3.lesson.notebook October24,2008 5.3...

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5.3.lesson.notebook 1 October 24, 2008 Oct 22­4:36 PM 5.3 Graphing Rational Functions Example #1: Consider the following reciprocal functions: SET A - linear denominators (ie. reciprocals of linear functions) f(x) = 2x - 3 g(x) = 1/(2x - 3) f(x) = -0.5x +1 g(x) = 1/(-0.5x + 1) Note: the function has opposite end behaviour with a min of one zero, V.A.(vertical asymptotes) occur when H.A. (horizontal asymptotes) occur at Oct 22­5:12 PM SET B - quadratic denominators (ie. reciprocals of quad. functions) f(x) = (x - 1) 2 - 3 g(x) = 1/(x - 1) 2 - 3 f(x) = -(x - 2) 2 + 3 g(x) = 1/-(x - 2) 2 + 3 Note: the function has the same end behaviour with a min of no zeros, V.A.(vertical asymptotes) occur when H.A. (horizontal asymptotes) occur at Oct 22­8:07 PM f(x) = (x + 2) 2 g(x) = 1/(x + 2) 2 SET B (continued) - quadratic denominators f(x) = (x + 2) 2 + 2 g(x) = 1/(x + 2) 2 + 2 Note: the function has the same end behaviour with a min of no zeros, V.A.(vertical asymptotes) occur when H.A. (horizontal asymptotes) occur at Oct 22­8:13 PM Example #2: Consider rational functions with a linear numerator and denominator of the form:

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