From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Continuity of Functions

Continuity of Functions

At a Glance - 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, 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.

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)
  • (fg)

People who Shmooped this also Shmooped...

Advertisement