What are continuous and discontinuous functions?
In this post, we distinguish between continuous and discontinuous functions, identifying key elements that distinguish each type of function, as a part of the Prelim Maths Advanced course under the topic Calculus and sub-part Gradients of Tangents.We learn to sketch graphs of functions that are continuous and compare them with graphs of functions that have discontinuities, describing the continuity informally, and identifying the continuous functions from their graphs.
A continuous function is a function that can be drawn without lifting your pen off the paper while making no sharp changes, an unbroken, smooth curved line. While, a discontinuous function is the opposite of this, where there are holes, jumps, and asymptotes throughout the graph which break the single smooth line.
The video below helps define and visual the definition of continuous, discontinuous and piecewise functions.
How do we determine if a function is continuous?
This video gives a three-step method on how you are able to determine if a function is discontinuous or not.