Limits at discontinuities


Plot a rational function that is undefined at x=-1 but yet whose limit as x approaches -1 exists.

Suppose is a rational function of the form , where does not factor , and is a positive integer. If is even, what can you say about and ?

Plot a rational function below with the following properties:
  • is defined everywhere except at , , and .
  • does not exist.
  • .
  • .

Suppose is a function equal to if and equal to if . What value of makes continuous at ?