SOLUTION: Give an example of a relation that is NOT a function and explain why it is not a function. I do not understand how to do this...please help its algebra.

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Question 480188:
Give an example of a relation that is NOT a function and explain why it is not a function.
I do not understand how to do this...please help its algebra.

Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20055) (Show Source):
You can put this solution on YOUR website!
The equation
x = y�
is not a function because both (1,1) and (1,-1) satisfy the
equation, and a function by definition cannot have two
different y-values for the same x value.
To make a graph of y� = x, make a table of values:
x | y
9 | 3
9 |-3
4 | 2
4 |-2
1 | 1
1 |-1
0 | 0
plot the points:

Connect them:

Also notice that it does not pass the vertical line
test. Below I have drawn three vertical lines which
intersect the curve twice. This cannot happen if
the graph is that of a function.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
a function is defined as an equation where every value of x has one and only one value of y.
y = x^2 would be a function.
the graph would look like this:

the graph of y = +/- sqrt(x) would be a relation because each value of x can have more than one value of y.
this occurs everywhere except at the vertex of the graph.
that graph looks like this:

you can see that this graph has 2 values of y for each value of x except at the vertex which is at x = 0.
note that in order for an equation to be a function, every value of x must have one and only corresponding value of y.
if only 1 value of x has more than 1 value of y, then the equation is a relation and not a function.
here's a reference that discusses the relationship between relations and functions.
http://www.purplemath.com/modules/fcns.htm