# How do you find discontinuity algebraically?

##### 1 Answer

There is no universal method that works for all possible functions.

The problems beginning calculus students are presented usually involve either:

Rational functions and trigonomeric functions are continuous on their domain. (dincontinuous when we try to divide by

Piecewise defined functions **may** be discontinuous where the rule changes. Check to be sure the limits from left and right are equal. And that these limits are equal to the value of the function at the

Examke 1

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**Example 2**

Because the left and right limits are equa, we have:

**But** the function is not defined for **at**

**Example 3**

**Example 4**