Continuity — Introduction to Continuous Functions + 5 more topics

A function $f(x)$ is continuous at a specific point $x = c$ if three conditions are met:

Photo by Gustavo Fring on Pexels

For piecewise functions, we're primarily concerned with the points where the function's definition changes. These are called break points or transition points.

Photo by Towfiqu barbhuiya on Pexels

Photo by RDNE Stock project on Pexels

When we talk about continuity, we mean a function whose graph you can draw without lifting your pen. When a function isn't continuous at a certain point, we call that a discontinuity. We'll focus on two main types: removable and jump.

Photo by Вадим Биць on Pexels

When we talk about continuity, we're essentially asking if a function is "smooth" and connected everywhere. If it's not, it's discontinuous. There are three main types you'll encounter:

Photo by Steve A Johnson on Pexels