Continuous Function

Definition

A continuous function is one that has no breaks, holes, or jumps in its graph. It can be drawn without lifting the pen from the paper.

Related terms

Discontinuous Function: A discontinuous function has one or more breaks, holes, or jumps in its graph. It cannot be drawn without lifting the pen from the paper.

Intermediate Value Theorem:

This theorem states that if a continuous function takes on two different values at two points within an interval, then it must also take on every value between those two points within that interval.

Limit:

The limit of a function represents what value it approaches as the input gets arbitrarily close to a certain point. It helps determine behavior near points of discontinuity and infinity.