review the graph of a piece - wise function. at which value of x does the function have a jump…

Explanation:

Step1: Recall jump - discontinuity definition

A jump discontinuity occurs when the left - hand limit and the right - hand limit of a function at a point exist but are not equal.

Step2: Analyze the graph at (x=-2)

The function is constant to the left of (x = - 2) and has a break at (x=-2), but it's not a jump as one of the limits is not well - defined in the context of the function's behavior around (x=-2) in terms of left and right limits for the sub - functions.

Step3: Analyze the graph at (x = 0)

The function has a smooth transition around (x = 0) (no break in the graph), so there is no discontinuity at (x = 0).

Step4: Analyze the graph at (x=1)

The function has a smooth transition around (x = 1) (no break in the graph), so there is no discontinuity at (x = 1).

Step5: Analyze the graph at (x = 3)

As (x) approaches (3) from the left, the function approaches a certain non - zero value. As (x) approaches (3) from the right, the function approaches a different non - zero value. The left - hand limit and right - hand limit exist but are not equal.

Answer:

3