SOLUTION: Is this equation a function or not? Why? f(x)= |x|

Question 436732: Is this equation a function or not? Why? f(x)= |x|
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
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:

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