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