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More on Graphs of Rational Functions

Video Summary:

A comprehensive graph of a rational function will exhibits these features: all intercepts, both x and y; location of all asymptotes: vertical, horizontal, and/or oblique; the point at which the graph intersects its non-vertical asymptote (if there is such a point); enough of the graph to exhibit the correct end behavior (i.e. behavior as the graph approaches its nonvertical asymptote). To find asymptotes of a rational function defined by a rational expression in lowest terms, use the following procedures: Vertical Asymptotes Set the denominator equal to 0 and solve for x. If a is a zero of the denominator but not the numerator, then the line x = a is a vertical asymptote. Other Asymptotes Consider three possibilities: If the numerator has lesser degree than the denominator, there is a horizontal asymptote, y = 0 ( the x-axis).



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