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Rational Functions :Rational Functions Section 4.4
Domain of Rational Functions :Domain of Rational Functions The domain of a artional function is the set of all real numbers that are not zeros of its denominator.
Intercepts of Rational Functions :Intercepts of Rational Functions If f has a y-intercept, it occurs at f(0).
The x-intercepts of the graph of a rational function occur at the numbers that
are zeros of the numerator
are not zeros of the denominator
The Big-Little Concept :The Big-Little Concept If c is a number far from 0, then is a number close to 0.
If c is close to 0, then is far from 0.
Vertical Asymptotes :Vertical Asymptotes A rational function has a vertical asymptote at x = c, provided
c is a zero for the denominator
c is not a zero of the numerator
Holes :Holes Let be a rational function and let d denote a zero of both g and h.
If the multiplicity of d as a zero of g is greater than or equal to its multiplicity as a zero of h, then the graph of f has a hole at x = d.
Otherwise, the graph has a vertical asymptote at x = d.
Horizontal Asymptotes :Horizontal Asymptotes Let be a rational function
whose numerator has degree n and whose denominator has degree k.
If n k, then there is no horizontal asymptote. To determine the end behavior, divide.
Graphing Rational Functions :Graphing Rational Functions Analyze the function algebraically to determine its vertical asymptotes, holes, and intercepts.
Determine the end behavior of the graph.
If the degree of the numerator is less than or equal to the degree of the denominator, find the horizontal asymptote.
Otherwise, divide the numerator by the denominator. The quotient is the nonvertical asymptote of the graph.
3. Use the preceding info. to select an appropriate viewing window to display a graph on your calculator.