Algebra Question?

Question

How woulg you graph y = | 3 - y |
(ABSOLUTE VALUE)

How would you get "y=" form for : x = | 3 - y| and x = y

Answer 1

y = |3 - x| means

y = 3 - x for 3 - x ≥ 0 ie x ≤ 3
and y = - (3 - x) for 3 - x < 0
= x - 3 for x >3

This would be the parts of two lines y = 3 - x and y = x - 3 that would always be on or above the x-axis and they would meet in the point of a V at x = 3

x = |3 - y|
So x = 3 - y for 3 - y ≥ 0
ie y = 3 - x for y ≤ 3
and x = -(3 - y) for 3 - y < 0
ie y = x + 3 for y > 3

So x = |3 - y| is the same as:

y = 3 - x for y ≤ 3
= x - 3 for y > 3

Answer 2

anthing in quadrants 3 and 4 would be reflected above the x axis
x = 3-y and x = -(3-y)
y = 3-x and y = x + 3