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

Explanation:

Step1: Recall continuity criteria

A function is continuous at a point $x = a$ if $\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)=f(a)$.

Step2: Analyze the graph at $x = 0$

Looking at the graph, as $x$ approaches $0$ from the left - hand side, the function value approaches a non - existent value at the open - circle point. As $x$ approaches $0$ from the right - hand side, the function value approaches the value at the closed - circle point. Since the left - hand limit and the right - hand limit are not equal at $x = 0$, the function is discontinuous at $x = 0$.

Answer:

B. not continuous at $x = 0$