You know it never occurred to me that the function would not have a discontinuity at $\displaystyle x=0$.

But I have reviewed about ten different calculus texts, and they are about evenly split on what it means. What did not occur to me is discontinuity may not meannot continuous at

We say a function has property $\displaystyle \mathcal{C}$ if and only if $\displaystyle A, ~B,\&~C$

So a function does not have property $\displaystyle \mathcal{C}$ if and only if $\displaystyle \neg A \vee \neg B \vee \neg C$.

So once again, read your textbook. You may not have missed points on that question.