A function is continuous at a number \(a\) if
\[ \lim_{x\ \to a }(f(x)) = f(a)\]
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:
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.
The solution is discussed in the video below.