What is a jump discontinuity of a graph?

Answer 1

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

Suppose #f(x)# is a real-valued function such that:
#{ (lim_(x->a^-) f(x) = u), (lim_(x->a^+) f(x) = v), (u != v) :}#
Then #f(x)# is said to have a jump discontinuity at #x=a#

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 #x=0#, with:
#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 #f(x)# at a jump discontinuity in order to make #f(x)# continuous.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

A jump discontinuity of a graph occurs when there is a sudden, non-continuous change in the function's value at a specific point. This means that the graph has a gap or jump at that point, where the function's value on one side of the point is different from the value on the other side.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7