Answer:
Piecewise functions are those where the behavior of the functions is dependent on the value of x.
For example the absolute value function f(x) = |x| is the same as
f(x) = -x , x<0
= x, 0<=x
To evaluate the value of f(x) = |x|, first determine if x is less than 0, equal to 0 or greater than 0. If x is less than 0, the value of |x| is equal to the negative value of x. In all other cases it is equal to the value of x.
This is the simplest piecewise function. There are other more complex functions where the function can take on more than 2 different behaviors based on the value of x.
Piecewise functions can also be identified from their graph. These have breaks in their graph, and each segment has a different behavior that is dependent on the value of x.
The evaluation of piecewise functions is done in the following way.
- First, look at x and determine from the available behaviors which one would be followed for that particular value of x.
- Next, we substitute x in that sub-function and determine the value obtained.
This complexity of this process varies with the piecewise function being evaluated. There are many functions which have a graph of infinite pieces.
A piecewise function is a function made up of different parts. More specifically, it’s a function defined over two or more intervals rather than with one simple equation over the domain. It may or may not be a continuous function.
