Question

Explain the meaning of continuity as it pertains to a function. Identify and explain the three conditions that must exist in order for a function to be continuous at a given point.

Answer 1

When there are no gaps or breaks on the graph, a function is continuous. When a function fails to be continuous, it is said to be discontinuous at that location.

What is Continuity in Calculus?

A function is continuous when there are no gaps or breaks in the graph. These gaps or breaks can be easily seen in a graph. They are also easily stated as holes, jumps, or vertical asymptotes. However, in calculus, you must be more specific in your definition of continuity.

There are three conditions that must be met in order to state a function is continuous at a certain point.

A function f(x) is continuous at a point a if only if the following three conditions are satisfied:

1.)f(a) is defined

2.)lim x→a f(x) exists

3.)lim x→a f(x)=f(a)

Therefore,  A function is discontinuous at a point a if it fails to be continuous at a.

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