Question

question 5 (1 point) the graph of a function f(x) is given below: there is a removable discontinuity at which of the following points (choose all that apply): x = 3 x=-1 x = 1

Explanation:

Step1: Recall removable - discontinuity definition

A removable discontinuity occurs when the limit of the function exists at a point, but the function is not defined or has a different value at that point. Graphically, it appears as a hole in the graph.

Step2: Analyze the graph at \(x = 3\)

The graph has a hole at \(x = 3\). The left - hand limit and the right - hand limit as \(x\to3\) are equal, but the function is not defined at \(x = 3\), so there is a removable discontinuity at \(x = 3\).

Step3: Analyze the graph at \(x=-1\)

The graph has a jump at \(x=-1\). The left - hand limit and the right - hand limit as \(x\to - 1\) are not equal. This is a non - removable (jump) discontinuity, not a removable one.

Step4: Analyze the graph at \(x = 1\)

The graph has a hole at \(x = 1\). The left - hand limit and the right - hand limit as \(x\to1\) are equal, but the function is not defined at \(x = 1\), so there is a removable discontinuity at \(x = 1\).

Answer:

\(x = 3\), \(x = 1\)