Special Graphs

Math
Summary

Asymptotes and Holes

Summary Asymptotes and Holes

Holes

When a value of x sets both the denominator and the numerator of a rational function equal to 0, there is a hole in the graph; that is, a single point at which the function has no value. f (x) = has a hole at x = 2:

f (x) =


Examples: Name the vertical asymptotes and holes in the graphs of the following equations:

  1. f (x) =
  2. f (x) =
  3. f (x) =

Solutions:
  1. Asymptotes: x = 3, - 3. Holes: x = - 4.
  2. Asymptotes: x = 2. Holes: x = 0.
  3. Asymptotes: x = - 1,, - 12. Holes: NONE.