|y|=x explain why it is not graph of function of x

Question

I don't know how to answer this

Answer 1

Recall that the absolute value of any number is always positive.  This means that the domain (which is set of x values) is all real positive numbers including zero.  The y values can be both positive and negative because y is inside absolute value symbol.  So if you were to graph this function, you get an absolute value curve that opens rightward with vertex at (0, 0).  This curve fails the vertical line test.

 

Here are two points to illustrate this failed vertical line test.

 

(1, 1) and (1, -1)

 

 

These two points have y values sharing the same x value.

Answer 2

1. Assuming y ≥ 0, y = x

2. Assuming y < 0, -y = x, y = -x

Now graph to answer your question.