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

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

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. Furthermore, …

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 exists). …

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. We’ll review types of …

17 hours ago · 1.3 Continuity Learning Objectives Apply the three conditions for continuity to determine whether a function is continuous or discontinuous at a given point. Identify and describe the three …

Generally, common functions exhibit continuity within their domain. Explore the concept of continuity, including asymptotic and jump discontinuities, and learn how to identify continuous functions in …

Here are some properties of continuity of a function. If two functions f (x) and g (x) are continuous at x = a then. f + g, f - g, and fg are continuous at x = a. f/g is also continuous at x = a provided g (a) ≠ 0. If f …

To determine if a function is continuous or differentiable, we can follow these steps: f (a) is defined. The limit lim x → a f (x) exists. lim x → a f (x) = f (a). Check: For a function to be continuous over an …

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 to determine if …