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 - Continuity on an Interval

Now that we've got the idea of a continuity at a point down, we can talk about what it means for a function to be continuous on an entire interval.

It shouldn't come as much of a surprise that we say a function f is continuous on the open interval (a,b) if f is continuous at every point c in (a,b), not including the points a and b.

In other words, f is continuous at every point in the interval (a, b).

If we try to graph a continuous function on this interval, we'll be able to draw a nice smooth curve from a to b without ever taking our pencil off the paper. We're going from Point A to Point B completely uninterrupted.

People who Shmooped this also Shmooped...