SOLUTION: 1. y² = x+1, 2. y² = 3-2x, and 3. x = |y| are not functions, give reasons and what does the graph x = |y| look like?

A function must not have two or more solutions in which the
output (y-value) are different for the same input (x-value).


1. y² = x+1 is not a function because 
(x,y) = (3,2) and (x,y) = (3,-2) are both
solutions, and there are two different
outputs (y-values), 2 and -2, for the same
input (x-value) of 3.

To show that both (3,2) and (3,-2) are solutions:

  y² = x+1        y² = x+1
(2)² = 3+1     (-2)² = 3+1 
   4 = 4           4 = 4


2. y² = 3-2x

is not a function because (x,y) = (-11,5) and 
(x,y) = (-11,-5) are both solutions, and there 
are two different outputs (y-values), 5 and -5, 
for the same input (x-value) of -11.

To show that both (-11,5) and (-11,-5) are solutions:

  y² = 3-2x           y² = 3-2x
(5)² = 3-2(-11)    (-5)² = 3-2(-11) 
  25 = 3+22           25 = 3+22
  25 = 25             25 = 25

3. x = |y| is not a function because for 
example, (x,y) = (3,3) and (x,y) = (3,-3) 
are both solutions, and there are two 
different outputs (y-values), 3 and -3, 
for the same input (x-value) of 3.

To show that both (3,3) and (3,-3) are solutions:

   x = |y|         x = |y|
   3 = |3|         3 = |-3| 
   3 = 3           3 = 3

To get the graph of x = |y|

Get some points  

x | y
0 | 0
1 | 1
1 |-1
2 | 2
2 |-2
3 | 3
3 |-3
4 | 4
4 |-4



Then draw the graph:



You can tell from the graph that it is not a function because 
it is possible to draw a vertical line through the graph and
it will intersect the graph more than once, like the green vertical
line below that intersects the graph twice:


 
Edwin