A function is continuous when its graph is a single unbroken curve ... that you could draw without lifting your pen from the paper.

Jul 12, 2021 · Try out these step-by-step pre-calculus instructions for how to determine whether a function is continuous or discontinuous.

Jun 6, 2025 · Identify any points where the function might be undefined. Check continuity at those specific points. Verify that the rest of the interval has no interruption in function values. …

Sep 27, 2023 · Checking the continuity of a function is easy! The simple rule for checking is tracing your pen on the curve. If you have to pick up your pen, the function is discontinuous. …

In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes …

Find out how to tell if a function is CONTINUOUS at a point. Determining continuity or where a function is Discontinuous. This using limits in the process ...

Nov 22, 2025 · Formally, a function f (x) is continuous at a point x = a if three conditions hold: f (a) is defined (the function has a value at a). lim⁡x→a f (x) exists (the limit from both sides …

Nov 16, 2022 · In this section we will introduce the concept of continuity and how it relates to limits. We will also see the Intermediate Value Theorem in this section and how it can be used …

A function f (x) is said to be a continuous function at a point x = a if the curve of the function does NOT break at the point x = a. Learn more about the continuity of a function along with graphs, …

Discover how to determine if a function is continuous on all real numbers by examining two examples: eˣ and √x. Generally, common functions exhibit continuity within their domain.