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Graphs of Rational Functions

Guidelines for Graphing Rational Functions

  1. Find the domain and range of the rational function.
  2. Find and plot the y-intercepts by finding f(0).
  3. Find and plot the x-intercepts by letting f(x)=0.
  4. Find and draw the vertical asymptotes The denominator of a rational function is equal to zero. .
  5. Find the discontinuities.
  6. Find and draw the horizontal asymptotes If m < n, the horizontal asymptote is y=0. If m = n, the horizontal asymptote is y = c/d, where c is the coefficient of the numerator and d is the coefficient of the denominator. If m > n, there is no horizontal asymptote. .
  7. Find and draw the slant asymptotes Slant asymptotes occur when the degree of the numerator is 1 more than the degree of the denominator. If you have a slant asymptote, you do not have a horizontal asymptote. The slant asymptote is the quotient when you divide the numerator by the denominatoe. .
  8. Find the intervals of increasing and decreasing.
  9. Find the minimum and maximum points.
  10. Test for symmetry.

Sketch and Graph a Rational Function

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