**Removable Discontinuity:** A removable discontinuity is a point on the graph that is undefined or does not fit the rest of the graph. There is a gap at that location when you are looking at the graph. Rational functions are discontinuous when the denominator equals zero. To find the removable discontinuity:

**How to Find:**

1. Factor the numerator and the denominator

2. Identify factors that occur in both the numerator and the denominator

3. Set the common factors equal to zero

4. Solve for x

5. Write your answers in the form x=

6. To find t=y plug the x values in the remaining parts of the equation

**Example:**

(has discontinuities at x=-2 and at x=3 so the denominator would be equal to zero.)

**Example:**

Solve for x:

(3)Solve for y:

(4)**Removable Discontinuity at**

**Jump Discontinuity:** If the left and right hand limits at x=a exist but disagree, then the graph jumps at x=a.

**Example:**

The point x=2 is a Jump Discontinuity.

**Infinite Discontinuity:**Exists when one of the one-sided limits of the function is infinite.

**Example:**The graph below shows a function that is discontinuous at x=a

Since the function never reaches a final value, the limit does not exist.