You’ll see a hole in the curve where the point discontinuity is. This usually looks like an unfilled circle. The point will be somewhere above or below the hole. For example, if you have the function f(x) = x, you expect a straight, diagonal line crossing through the origin. However, if there’s a hole in the curve at x = 3, and a point at (3, 10), the function is discontinuous.
For example, for f(x) = x, let’s say at x = 4, the f(x) = x curve ends with a hole. Then, at x = 4, a second curve of f(x) = x + 5 begins. This second line is disconnected and above the first line.
Where: f(x) is a function f(c) is the function value at x = c c is a given x value
Take the limit of f(x) = f(a) for x approaches a+ (a from the right). Take the limit of f(x) = f(b) from x approaches b- (b from the left).
