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. Furthermore, …

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 …

Dec 21, 2020 · Summary: For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the …

Nov 22, 2025 · In mathematics, continuity describes how smoothly a function behaves without sudden jumps, breaks, or holes. It is an important unit of Calculus as it forms the base, and it helps us further …

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 in value, known …

Apr 29, 2025 · Determine if f (x) is continuous at x = 1. Solution: First, simplify the function: Now find the limit: But f (1) = 3. Thus, lim x → 1 f (x) ≠ f (1). Type: Removable Discontinuity (the function has a …

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 …

Sep 28, 2025 · We’ll unveil 5 analytical ways to definitively determine if a function is continuous, leveraging the power of limits and algebraic manipulation – essential skills for every US math student.