# What is a jump discontinuity of a graph?

##### 1 Answer

Apr 27, 2018

A point in the graph of a function where left and right limits exist but differ.

#### Explanation:

Suppose

#{ (lim_(x->a^-) f(x) = u), (lim_(x->a^+) f(x) = v), (u != v) :}#

Then

For example, consider:

#f(x) = { (x + x/(abs(x)) " for " x != 0), (0 " for " x = 0) :}#

graph{x+x/abs(x) [-10, 10, -5, 5]}

This has a jump discontinuity at

#lim_(x->0^-) f(x) = -1#

#lim_(x->0^+) f(x) = 1#

Unlike a hole (a.k.a. removable discontinuity), there is no replacement value that we can assign to