Question

find the x - value(s) where the graph is not continuous.
the x - value(s) where the function is not continuous is/are ( x=square ).
(use a comma to separate answers as needed.)

Explanation:

Step1: Recall the definition of continuity

A function \(y = f(x)\) is continuous at \(x = a\) if \(\lim_{x
ightarrow a^{-}}f(x)=\lim_{x
ightarrow a^{+}}f(x)=f(a)\). Discontinuities occur when this condition is violated.

Step2: Analyze the graph

Looking at the graph, we check for points where there are breaks, jumps, or holes.

• At \(x = 2\), there is a hole (the left - hand limit and the right - hand limit exist but \(f(2)\) is not equal to the limit of the function as \(x\) approaches \(2\)).
• At \(x = 6\), there is a hole (the left - hand limit and the right - hand limit exist but \(f(6)\) is not equal to the limit of the function as \(x\) approaches \(6\)).

Answer:

\(2,6\)