Question

Why isn't |y| = 4-x not a function?

Answer 1

y = |4 - x| is function but |y| = 4-x isn't a function...I just dont know why? anyone?

Answer 2

It's not a function because it fails the vertical line test. In other words there could be two values of \(y\), for the same \(x\). Take \(x=0\) as an example. \(|y|=4-0 \implies y=4\text{ or } y=-4\). So, f(0) has two values and therefore it's not a function.

Answer 3

Anytime I work with absolute values, I try to think of them as two functions in this case |y|=-y and |y|=y. Since one of your y's is negative you should multiply the other side of the equation by -1 to get -1(4-x) or -4+x. You can see that y=-4+x and 4-x.