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Graphing Rational Functions. Rational Function. Where N(x) is the numerator polynomial and D(x) is the denominator polynomial. Domain: all real numbers except where the denominator equals zero. Parent Function - , where . RATEY: tool to graph rational functions.
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Rational Function • Where N(x) is the numerator polynomial and D(x) is the denominator polynomial. • Domain: all real numbers except where the denominator equals zero. • Parent Function - , where
RATEY: tool to graph rational functions • R: roots where • A: asymptotes…vertical set • T: togetherness determine the direction of the branches by picking test points around the asymptotes • E: end behavior…horizontal asymptotes • Y: y-intercepts set and solve for y
Vertical Asymptotes: • Set the denominator equal to zero. • Solve for x. • Written as x =
Horizontal Asymptotes: • Identify the highest power in the numerator & denominator. • If the numerator power is higher than the denominator power, then there is no horizontal asymptote. • If the numerator power is equal to the denominator power, then the horizontal asymptote is the coefficients in front of the highest powers (y = a/b). • If the numerator power is lower than the denominator power, then the horizontal asymptote is y = O.
Horizontal Asymptotes: N(x) > D(x) no horizontal asymptote N(x) = D(x) y = a/b N(x) < D(x) y = O
Graph the Rational FunctionStep I: Factor and find all the informationEx 1. • R- roots • A – vertical asymptotes • T – togetherness • E – horizontal asymptotes • Y – y-intercepts
Graph the Rational FunctionStep II: Graph using the informationyou found in Step IEx 1.
Graph the Rational FunctionStep I: Factor and find all the informationEx 2. R- roots A – vertical asymptotes T – togetherness E – horizontal asymptotes Y – y-intercepts
Graph the Rational FunctionStep II: Graph using the informationyou found in Step IEx 2.
