Question

the graph below is the function f(x)
determine which one of the following rules for continuity is violated first at x = 2.
○ f(a) is defined.
○ lim(x→a) f(x) exists.
○ lim(x→a) f(x)=f(a).

Explanation:

Step1: Check if \(f(a)\) is defined at \(a = 2\)

The graph has an open - circle at \(x = 2\), which means \(f(2)\) is not defined.

Step2: Analyze other continuity conditions

Since \(f(2)\) is not defined, we don't need to check if \(\lim_{x
ightarrow2}f(x)\) exists or if \(\lim_{x
ightarrow2}f(x)=f(2)\) as the first condition for continuity is already violated.

Answer:

\(f(a)\) is defined.