MATH-UA 121 Lecture Notes - Lecture 5: Asymptote
22 Sep 2016
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Use this for rational functions or else you get. If the degree of the numerator = the degree of the denominator, the horizontal asymptote equals. If the degree of the numerator < the degree of the denominator, the horizontal asymptote is y = 0. Graphing rational functions: domain, asymptotes, intercepts, symmetry, extrema, increasing/decreasing, concavity, point of inflection. Good order for graph sketching: asymptotes, intercepts, extrema, points of inflection, use steps 5 and 6 to shape the curve. The absolute maximum of a function on an interval is the greatest value on the interval. The absolute minimum of a function on an interval is the smallest value on the interval. Extreme value theorem: if a function is continuous on a closed interval (no holes or asymptotes) [a, b] then f has both an absolute minimum and an absolute maximum on the interval.
