Question

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

Explanation:

Step1: Recall the definition of a continuous function

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

Step2: Analyze the given graph

Looking at the graph, there are jumps (discontinuities) in the graph. For example, at the points where the different line - segments meet, the left - hand limit and the right - hand limit do not match.

Answer:

A. not continuous