Math basics › Functions and graphs

Asymptotes

Vertical

Where the bottom of a fraction is zero and the top is not. The graph shoots off and never touches the line.

Horizontal

What happens as x runs off to ±∞. Compare degrees: bottom bigger gives y = 0, equal gives the ratio of leading coefficients, top bigger gives no horizontal asymptote.

Holes

If a factor cancels from top and bottom, that is a hole, not an asymptote.