Continuous
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A function is continuous if you can draw its graph without lifting your pencil from the paper. For a function to be continuous at a specific point:
The function has to have a value at that point. This means the function is actually defined there.
You need to be able to get close to that value from both sides of the point. As you move closer to the point from either side, the function values should get closer to a specific number.
The value of the function at that point should match the number you get as you approach it. Basically, the function’s value at that point should be the same as the value you’re approaching from both sides.
In short, for a function to be continuous at a point, the graph should be smooth and not have any jumps, holes, or breaks there.