# Continuity of Functions

# Determining Continuity

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,* e*^{x}, 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.