Zeros of a function

What is a zero of a function? The best definition I can give you is that a zero of a function is a variable that makes the function equal to zero when it is plugged in. For example if you needed to find the zero of x +8= 0, the zero of the function would be -8. Because -8 +8 = 0. For equations like this, that involve addition or subtraction, the zero is usually the opposite number(the negative). When the function involves multiplication or division the zero itself is just zero. Zeros of the function are important because it shows us where on the x-axis the function intersects. 

Peace-wise functions

Peace wise functions use more then one equation per graph. We do his to find if the equation is continuous or discontinuous. If there's no holes or gaps or you can draw it with one line, then the functions are continuous. If not then the function are discontinuous. 

The greatest integer function so represented by an x between two double brackets. 

Looks a little something like this. Except for the fact that the lines normally go on and on. This is just a shortened version.  There isn't really a main reason for having these functions, but the main, probably only point is to find whether the graph is continuous or nah.