A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f (x) where f (x) = -9 when -9 < x ≤ -5, f (x) = 6 …

A piecewise function is a function that is defined in separate "pieces" or intervals. For each region or interval, the function may have a different equation or rule that describes it. We can graph a …

We learn that to find one-sided and two-sided limits, we need to consider the function definition for the specific interval we're approaching and substitute the value of x accordingly.

We examine a piecewise function to determine its continuity and differentiability at an edge point. By analyzing left and right hand limits, we establish continuity.

Practice Limits by direct substitution Get 3 of 4 questions to level up! Direct substitution with limits that don't exist Get 3 of 4 questions to level up! Limits of trigonometric functions Get 3 of 4 …

Piecewise functions piece together different functions. Absolute value graphs make a V shape, but why do they do that? Let's explore how to make some new and interesting types of graphs. …

Discover how to make a function continuous by determining the appropriate value for a discontinuous point. In this example, we explore the function f (x) = (6x² + 18x + 12) / (x² - 4) …

Continuity requires that the behavior of a function around a point matches the function's value at that point. These simple yet powerful ideas play a major role in all of calculus.

Finding the domain and range of a piecewise function where each segment is linear.

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