mac1140_lecture20_1

# mac1140_lecture20_1 - L20 4.5 Rational Functions *See...

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172 L20 §4.5 Rational Functions **See Appendix for important graphs you need to memorize** Definition : A function of the form () p x fx qx = , where ( ) p x and ( ) are polynomials, is called a rational function . Recall : The rational function f is undefined whenever The rational function f is equal to zero whenever The domain of the rational function f is Important: When working with a rational function, first factor the numerator and denominator and give the domain , and then reduce it to the lowest terms.

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173 Example . State the domain and sketch the graph of the function 1 2 y x = . Vertical Asymptote (VA) : x a = is a VA, if () fx →∞ as x a . Note : In order to find vertical asymptotes , reduce a rational expression to the lowest terms. As soon as the expression is in the lowest terms, vertical asymptotes occur where__________________
174 Example. Find all vertical asymptotes. a) 23 () 1 x fx x = b) 2 2 4 x gx x + = Holes : At x a = the graph has a “hole” if a is a zero of the denominator, but the factor ( ) x a can be canceled out

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## This note was uploaded on 02/29/2012 for the course MAC 1140 taught by Professor Gregory during the Fall '11 term at Broward College.

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mac1140_lecture20_1 - L20 4.5 Rational Functions *See...

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