This is an example of a point discontinuity.
Example 7: Consider the following function: f(x) = .
The function is discontinuous because it’s possible for the denominator to equal zero (at x = 2). This
means that f(2) doesn’t exist, and the function has an asymptote at x = 2. In addition, f(x) = −∞ and
f(x) = ∞.The graph looks like the following:
This is an example of an essential discontinuity.