Question

How to know if a graph is continuous at a point ? (limits)

Answer 1

plugging the values into the formula of the graph will not give you infinity.

Answer 2

a function f(x) is said to be continuous at x = a if \[\lim_{x \rightarrow a}f(x) = f(a) \]
A function, f(x) is said to be continuous on the interval [a, b] if it is continuous at each point in the interval!

NOTE:
If f(x) ois continuous on x= a then
\[\lim_{x \rightarrow a}f(x) = f(a) \]\[\lim_{x \rightarrow a^+}f(x) = f(a) \]\[\lim_{x \rightarrow a^-}f(x) = f(a) \]