The correct option regarding the continuity of the function at x = 0 is given by:
A. The function is continuous.
The graph is missing, and is given at the end of this problem.
A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
From the graph of the function, at x = 0, we have that:
[tex]\lim_{x \rightarrow 0^-} f(x) = \lim_{x \rightarrow 0^+} f(x) = f(0) = 0[/tex]
Which means that the function is continuous at x = 0, hence option A is correct.
More can be learned about continuity of a function at https://brainly.com/question/24637240
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