Question

the graph of a function f is shown in the figure above. at what value of x does f have a removable discontinuity?

Explanation:

Step1: Recall definition of removable discontinuity

A removable discontinuity occurs when the limit of the function exists at a point but the function is not continuous there (hole in the graph).

Step2: Examine the graph

At \(x = 1\), the function has a hole. The left - hand limit and the right - hand limit as \(x\) approaches \(1\) exist and are equal, but the function is not defined at \(x = 1\).

Answer:

\(x = 1\)