Holes

Holes in a graph are denoted by a hollow circle, and show a point where the graph doesn't actually exist

left = -10; right = 10;
bottom = -10; top = 10;
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y = \frac{x^2 + 3x - 4}{x - 1}
(1, 5) | open | label: hole

Determine Hole or Asymptote

Let represent a factor in both the numerator and denominator of a rational function

• If the factor completely cancels out the denominator:
  • state the restriction, and note that there is a hole at
  • True when
• If not
  • There is an asymptote at
  • True when

Examples:

Asymptotes can be determined with the same methods as Rational Functions