Continuity on an Interval via Formulas
When we are given problems asking whether a function f is continuous on a given interval, a good strategy is to assume it isn't. Try to find values of x where f might be discontinuous.
If we're asked about the continuity of one function on several different intervals, find all the problem spots first and worry about which intervals they're in later.
If there aren't any such values in the interval, then the function is continuous on that interval.