Determining Continuity - At A Glance

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. The quotient won't be defined there.

Examples

Example 1

Let f(x) = 4x² + 3x and g(x) = sin(x). Determine whether each function is continuous. If not, where is the function discontinuous?

(f + g)
(f – g)

Show Next Step

Determining Continuity - At A Glance

Example 1

Tired of ads?