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The above statement looks like just one thing must happe for a function to be continuous at \(a\), but to check if a function is continuous, we need three conditions satisfied:

\(f(a)\) must be defined (\(a\) is in the domain of \(f\)).

\(\lim_{x \to a}f(x)\) exists (the right and left limits must agree).

\(\lim_{x \to a}f(x) = f(a)\).

Take a look at the picture below and try to determine if the function $f$ is continuous at \(x = 1,2,3\) and \(4\). If the functions is not continuous at one of the numbers, make a list of all of the above above conditions that the function does not satisfy.