9.3 - Warm-up Factor 9.3 Notes Rational Functions and Their...

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9.3 Notes Warm-up: Factor: OBJECTIVES: c Identify properties of rational functions c Graph rational functions An inverse variation is an example of a rational function! 24 19 2 2 + - = x x y Rational Function c Rational means – “ratio” which means “fraction”! Rational Function: where P(x) and Q(x) are polynomial functions and Q(x) is NOT zero. A polynomial divided by a polynomial Example: ) ( ) ( ) ( x Q x P x f = 1 2 ) ( 2 + - = x x x f Examples of graphs 1 2 ) ( 2 + - = x x x f 4 1 2 - = x y 1 ) 1 )( 2 ( ) ( + - + = x x x x f POINT OF DISCONTINUITY: Find the values of x that make the denominator = ? Finding Points of Discontinuity 1 2 1 2 + + = x x y 1) 2) 1 1 2 + + - = x x y Discontinuity: c Breaks: asymptotes create “breaks” in a graph. - where the denominator is equal to zero. Ex: c Holes: the same zero occurs in numerator and denominator. This x cannot occur – it creates a “hole” in our graph. Ex:

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9.3 - Warm-up Factor 9.3 Notes Rational Functions and Their...

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