Question 436732
The Absolute Value f (x) =|x| is  the function.

why?---There is only one y for each x.

|x| is what is known as the absolute value of x. It is defined by

|x|={ x if x  > or =0
|x|={ -x if x<0

For negative x it is the line y = - x (red on a graph below) and for positive x it is the line y = x (green on a graph below). Note that it turns through a right-angle at the origin.

The question ``What is the slope of y =|x| at the origin?'' does not seem to have a sensible answer. So we ought to find ourselves in difficulties if we try to differentiate f (x) =|x| at x = 0. 

Whenever you have an absolute value graph, the general shape will look like a “v” (or in some cases, an upside down “v”. 

here is the graph:
{{{ graph( 500, 500, -15, 15, -0, 15,-x, x) }}}