Understanding Removable Discontinuities | Explained with Examples and Simplified Function Explanation

Removable discontinuity

A removable discontinuity is a type of discontinuity that occurs in a function when a point in the graph can be “removed” or filled in with a continuous value to make the function continuous at that point

A removable discontinuity is a type of discontinuity that occurs in a function when a point in the graph can be “removed” or filled in with a continuous value to make the function continuous at that point.

In simpler terms, a removable discontinuity happens when there is a hole in the graph of a function, but if you were to fill in that hole with a single point, the function would become continuous at that point.

An example of a removable discontinuity can be seen in the function f(x) = (x^2 – 4)/(x – 2). If we try to evaluate this function at x = 2, we get 0/0, which is undefined. However, if we simplify the function by factoring the numerator, we can rewrite it as f(x) = (x + 2), except that there is still a hole at x = 2. In this case, we can see that the hole occurs because both the numerator and denominator have a factor of (x – 2), which cancels out when we simplify the function. By canceling this common factor, we can fill in the hole with a single point, and the function would become continuous at x = 2.

Removable discontinuities can also occur in other forms, such as rational functions, where factors in both numerator and denominator cancel out, or in piecewise functions, where different parts of the function are not connected at certain points.

To summarize, a removable discontinuity is a type of discontinuity that can be “removed” or filled in with a continuous value to make the function continuous at that point. It typically occurs when there is a hole in the graph that can be “patched up” with a single value.

More Answers: