determine if the function below is continuous.\na. not continuous at x = 0\nb. not continuous at x = 1\nc…

Explanation:

Step1: Recall continuity definition

A function is continuous at a point if the limit as $x$ approaches that point from the left equals the limit as $x$ approaches that point from the right and equals the function - value at that point.

Step2: Analyze the graph at $x = 0$

Looking at the graph, there is a break at $x = 0$. The left - hand limit and the right - hand limit as $x$ approaches $0$ are not equal to the function value at $x = 0$ (there is a hole at $x = 0$).

Step3: Analyze the graph at $x = 1$

The function is smooth and unbroken at $x = 1$. The left - hand limit, right - hand limit, and function value are equal at $x = 1$.

Step4: Analyze the graph at $x=-1$

The function is smooth and unbroken at $x=-1$. The left - hand limit, right - hand limit, and function value are equal at $x=-1$.

Answer:

A. not continuous at $x = 0$