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M1330_section2.3

# M1330_section2.3 - Section 2.3 Rational Functions and Their...

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Section 2.3 – Rational Functions 1 Section 2.3 Rational Functions and Their Graphs A rational function can be expressed as ) ( ) ( ) ( x q x p x f = where p ( x ) and q ( x ) are polynomial functions and q ( x ) 0. Vertical Asymptote of Rational Functions The line x = a is a vertical asymptote of the graph of a function f if f ( x ) increases or decreases without bound as x approaches a . Example: Given the graph of x x f 1 ) ( = . Locating Vertical Asymptotes and Holes Factor the numerator and denominator. Look at each factor in the denominator. If a factor cancels with a factor in the numerator, then there is a hole where that factor equals zero. If a factor does not cancel, then there is a vertical asymptote where that factor equals zero. Example 1: Find any vertical asymptotes and/or holes of 6 10 3 ) ( 2 2 - - - - = x x x x x f .

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Section 2.3 – Rational Functions 2 Horizontal Asymptote of Rational Functions The line y = b is a horizontal asymptote of the graph of a function
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M1330_section2.3 - Section 2.3 Rational Functions and Their...

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