What is continuity?

A function f(x) is continuous at a given point (x = a) if its limits from the left-hand (a-) and right-hand (a+) sides are the same value as the specific point on the function where x = a.

Sometimes in calculus, we'll work with functions that at a given point, don't make a complete, continuous path.

Scenario: Imagine the function displayed on this coordinate plane represents a road. A storm damaged the road, and at x = a, the road disconnects. Interpret the road's continuity.

Although the function, at x = a, has a value of y = b...

...the function is not continuous at that point!

From the left, our function approaches y = c.

From the right, our function approaches y = b.

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