Function and the graph

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					                   Rational Functions – Everything you need to know to graph

Function and the graph     Real Roots: Set the       Vertical Asymptote: Set    Domain: x ≠ whatever the   Horizontal Asymptotes:
                           numerator equal to zero   the denominator equal to   vertical asymptote is      n < m then y = 0
f(x) = xn + xn-1 + … + a   and solve for x.          zero and solve.                                       n = m then y = the
       xm +xm-1 + … + b                                                                                    leading coefficients
                                                                                                           n > m then none
           x3
f(x) =
         x  5x  4
          2




         x 1
f(x) =
         x4




       x 2  3x  2
f(x) =
           x5
                    Rational Functions – Everything you need to know to graph

Function and the graph     Real Roots: Set the       Vertical Asymptote: Set    Domain: x ≠ whatever the   Horizontal Asymptotes:
                           numerator equal to zero   the denominator equal to   vertical asymptote is      n < m then y = 0
f(x) = xn + xn-1 + … + a   and solve for x.          zero and solve.                                       n = m then y = the
       xm +xm-1 + … + b                                                                                    leading coefficients
                                                                                                           n > m then none
         2x 2  3
f(x) =
         x2  4




         x3
f(x) =
         x2  8




         x 2  5x
f(x) =
           x2
Rational Functions – Everything you need to know to graph

				
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Lingjuan Ma Lingjuan Ma
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