From: Marielouise (for Teacher2Teacher Service)
Date: Mar 25, 2001 at 17:27:09
Subject: Re: determination of a relation to a function

Hi, Kara,

A resource for you can be found in:

Relations versus functions
http://mathforum.org/dr.math/problems/nicole10.27.98.html

This is a Dr. Math answer to "what is the difference between a relation
and a function?"

You asked about teaching this. Do you have access to graphics calculators?
If you do then:
1. Solve the equation for y   (You find that y = +/-(Sq root of (11-x)))

2. Put each of these in the calculator for y1 and y2.

3. You will notice that the graphs will only graph for values of 11-x >= 0
or when x =< 11.   This gives you a restricted domain.

4.  You will also notice for each value of x that you have less than or equal
11, there are two values of y.

5.  A relation is defined as a function when for each value of x allowed in
the rule, there is only ONE value of y.

Visually, you can see that when a vertical line is passed through the graph
there is more than one point of intersection with the graph.

Suppose you do not have a calculator to do this for you. Then I suggest that
you graph it by hand selecting "good values of x" so that you get nice square
roots:
For example x = 11 gives you y = 0.  x = 2, y = +/-3, x = 7, y = +/- 2, etc.

When you connect the points, assuming continuity, you get a parabolic shape
that opens horizontally, rather than vertically.

If you need a good working definition of when there is a function try:

A function is a rule that is applied to allowable number so that only ONE
number results or is found. I include the word "allowable" number because
there are situations such as in your situation where not all values of x are
allowed or make sense in the equation.

 -Marielouise, for the T2T service

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