This curve looks very similar to a point discontinuity, but notice that with a removable discontinuity,
f(x) is not defined at the point, whereas with a point discontinuity, f(x) is defined there.Example 5: Consider the following function:
f(x) = The left-hand limit is 5 as x approaches 2, and the right-hand limit is 4 as x approaches 2. Because the
curve has different values on each side of 2, the curve is discontinuous at x = 2. We say that the curve
“jumps” at x = 2 from the left-hand curve to the right-hand curve because the left and right-hand limits
differ. It looks like the following:
This is an example of a jump discontinuity.
Example 6: Consider the following function:
f(x) = Because f(x) ≠ f(2), the function is discontinuous at x = 2. The curve is continuous everywhere except
at the point x = 2. It looks like the following: