Question

determine if the function below is continuous.
a. both continuous and not continuous
b. cannot be determined
c. continuous
d. not continuous
reset selection

Explanation:

Step1: Recall the definition of continuity

A function \(y = f(x)\) is continuous at a point \(x = a\) if \(\lim_{x
ightarrow a^{-}}f(x)=\lim_{x
ightarrow a^{+}}f(x)=f(a)\). Visually, a function is continuous if its graph has no breaks, holes, or jumps.

Step2: Analyze the graph

Looking at the given graph, there are breaks (holes and jumps) in the graph. For example, at some points, the left - hand limit, right - hand limit, and the function value (if it exists) are not equal.

Answer:

D. not continuous