That means that the functions is made up of different functions - for example, one function for one interval, and another function for a different interval. Such a function is still a legal function - it meets all the requirements of the definition of a "function". However, in the general case, you can't write it as "y = (some expression)", using a single expression at the right.
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A piecewise function is a function defined by two or more equations. A step functions is a piecewise function defined by a constant value over each part of its domain. You can write absolute value functions and step functions as piecewise functions so they're easier to graph.
Piecewise, linear, exponential, quadratic, Onto, cubic, polynomial and absolute value.
The form of the piecewise functions can be arbitrarily complex, but higher degrees of specification require considerably more user input.
A piecewise defined function is a function which is defined symbolically using two or more formulas
All differentiable functions need be continuous at least.