use the graph to answer the question. describe the continuity of the graphed function. (1 point) the…

Explanation:

Step1: Recall the definition of continuity and discontinuity

A function (y = f(x)) is continuous at (x=a) if (\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)=f(a)). A removable discontinuity occurs when (\lim_{x\rightarrow a}f(x)) exists but (f(a)) is not defined or (f(a)\neq\lim_{x\rightarrow a}f(x)). A non - removable (infinite or jump) discontinuity occurs when (\lim_{x\rightarrow a^{-}}f(x)\neq\lim_{x\rightarrow a^{+}}f(x)) (jump) or (\lim_{x\rightarrow a^{-}}f(x)=\pm\infty) or (\lim_{x\rightarrow a^{+}}f(x)=\pm\infty) (infinite).

Step2: Analyze the graph at (x = 0)

As (x\rightarrow0^{-}), (y\rightarrow-\infty) and as (x\rightarrow0^{+}), (y\rightarrow+\infty). So (\lim_{x\rightarrow0^{-}}f(x)) and (\lim_{x\rightarrow0^{+}}f(x)) do not exist in the finite sense (infinite discontinuity).

Step3: Analyze the graph at (x = 3)

The function is well - defined and smooth near (x = 3). There is no break, hole, or jump in the graph near (x=3).

Answer:

The function has a nonremovable discontinuity at (x = 0).