Learning Resources

Investigation3: Discontinuities and Vertical Asymptotes

Step B

Each graph has a point of discontinuity, or "hole," indicating the specific point for which the function is undefined. These holes correspond to places that make the function evaluate to . Generally speaking, if a factor is repeated in the numerator and denominator, then the zero of that factor identifies a point of discontinuity.

Note: There is no advance warning of the discontinuity here, just a sudden gap in the graph.

Be sure you can predict, upon examination of a function, when and where a point of discontinuity will occur.