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Topic

Rational Functions and Vertical Asymptotes Determine holes in graphs of rational functions. If the multiplicity of a real zero in the numerator is greater than or equal to its multiplicity in the denominator, then the graph of the rational function has a hole at the corresponding input value. 1.10.A.2 If the graph of a rational function r has a hole at x = c, then the location of the hole can be determined by examining the output values corresponding to input values sufficiently close to c. If input values sufficiently close to c correspond to output values arbitrarily close to L, then the hole is located at the point with coordinates (c L, ). The corresponding mathematical notation is lim r x( ) = L x c . It should be noted that lim r x( ) = lim r x( ) = lim r x( ) = L. − + x c x c x c