question 5 (1 point) the graph of a function f(x) is given below: there is a removable discontinuity at…

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

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

Answer

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)