When we say a function f is continuous, we usually mean it's continuous at every real number. In other words, it's continuous on the interval (-∞, ∞).
Some examples of continuous functions that are continuous at every real number are: polynomials, ex, sin(x), and cos(x).
If we add, subtract, multiply, or compose continuous functions, we find new continuous functions. If we take a quotient of continuous functions 
, this quotient will be continuous on any intervals that do not include places where g is zero. The quotient won't be defined there.
will be continuous on the intervals ..., (-2π, -π), (-π,0), (0,π), (π,2π),...
is continuous wherever f is not zero. 
, the function 
is continuous on the intervals 