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

Explanation:

Step1: Recall the definition of continuity

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 (i.e., (\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x))), but (f(a)) is either not defined or not equal to the limit. A jump discontinuity occurs when (\lim_{x\rightarrow a^{-}}f(x)\neq\lim_{x\rightarrow a^{+}}f(x)). An infinite discontinuity occurs when (\lim_{x\rightarrow a^{-}}f(x)=\pm\infty) or (\lim_{x\rightarrow a^{+}}f(x)=\pm\infty)

Step2: Analyze the graph

Looking at the graph, as (x) approaches (3) from the left and from the right, the function values approach the same non - infinite value. However, the point at (x = 3) on the graph has a hole (the open circle) which means the function is not defined at (x = 3) in the way it should be to match the limit.

Answer:

The function has a removable discontinuity at (x = 3)