Continuous, Discontinuous, and Piecewise Functions

The video tutorial covers continuous and discontinuous functions, explaining how continuous functions have no gaps and can be drawn without lifting a pencil. It introduces discontinuous functions, highlighting cases where certain x values are not valid inputs, leading to undefined points or asymptotes. The tutorial also discusses discontinuities like holes and jumps, using examples to illustrate these concepts. Finally, it explains piecewise functions, which are evaluated differently based on the input value, and demonstrates how to graph them.

What is the significance of a hole in the graph of a function?

Describe a piecewise function and provide an example.