Question

the graph of the function (f) is shown above. what are all values of (x) for which (f) has a removable discontinuity?
a 1 only
b 5 only

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 either undefined or has a different value at that point. This is often indicated by a hole in the graph.

Step2: Analyze the graph

Looking at the graph of \(y = f(x)\), we see a hole at \(x = 5\). The limit of \(f(x)\) as \(x\) approaches \(5\) exists (the left - hand and right - hand limits are equal), but the function is not continuous at \(x = 5\) because the function value at \(x = 5\) is not equal to the limit. There is no such hole at \(x = 1\).

Answer:

B. 5 only