Question 26362
A piece-wise defined function is when the function f(x) will be a certain equation according to the value of x and the applied conditions. Here's a problem for example:

Evaluate the following function at x= -2, -1, 1, and 3.

f(x) = 6-x  if x > 2
f(x) = 3x   if x < 2 

In other words, f(x) will only = 6-x if x is greater than 2. In addition, f(x) will only be 3x, if x is less than 2.

Now, starting with the first value for x which is -2, we see that it is less than 2. As a result the function applied is: f(x) = 3x

If we use, however, the value 3 for x, which is greater than two, the function is 6-x.

I hope you understand!