review the graph of a piecewise function. for which value of x is the function continuous? 1 -3 -1 3

Explanation:

Step1: Recall continuity condition

A function is continuous at a point if the left - hand limit, right - hand limit, and the function value at that point are equal.

Step2: Analyze $x = 1$

At $x = 1$, the left - hand limit and right - hand limit do not match the function value (there is a jump), so it is not continuous.

Step3: Analyze $x=-3$

At $x=-3$, the left - hand limit and right - hand limit and the function value are equal. The curve approaches the same value from both sides and the function is defined at that point.

Step4: Analyze $x = - 1$

At $x=-1$, there is a break in the graph, so it is not continuous.

Step5: Analyze $x = 3$

At $x = 3$, the left - hand limit and right - hand limit do not match (there is a jump), so it is not continuous.

Answer:

$-3$