Teacher2Teacher Q&A #6018

Determination of a relation to a function

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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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