When+is+a+function+continuous+at+a+point+x+=+a?

=﻿__When is a Function Continuous at a Point x=a?__=

Continuity
A function is continuous when a derivative exists for every input on the function except corners and cusps. The corners and cusps can be identified by finding the values at which the derivative of the function is undefined, then plugging the values into the function; if the output value is equal to the limit approaching the imput value, then there is a corner or cusp.

Example 1: Is IxI continous?

Answer: despite having a derivative of -1 from the left and 1 from the right, this function is continuous as F(0)=0 and the limit as x approaches 0 is 0