Finding Equations from Relations

Date: 01/06/98 at 23:36:08
From: ASAD KHAN
Subject: Homework

Dear Dr. Math,

Can you help me and give me simple steps for how to do a chapter in 
the book called "Finding Equations from Relations"? The homework 
questions that I need help on are below.

1. A = -2   -1	0	1	2
   B = -3    1	5  ___  ___
You are supposed to complete the chart and give an equation for B.

2. X =  1     2   3   4   5   6   7
   Y = 14    13  12  11  10   9   8
You are supposed to find an equation that makes the graph true.

3. A =  -5  -3  -1   1   2   4   7
   B =  25  18   8
You are supposed to complete the chart and give an equation for B.

4. R =  -4  -2   0   2   4   6   8
   S =  -1   0   1   2   3   4   5
You are supposed to find an equation that makes the graph true.

5. (-2, 4), (-1, 1), (0,0),(1, 1), (2,4)
You are supposed to write an equation to represent each relation.

6. (-6, 4), (-3,8), (1, -24), (2,-12), (6, -4)
You are supposed to write an equation to represent each relation.

7. (-4, 3), (-2,12), (-1, 48), (1,48), (2, 12)
You are supposed to write an equation to represent each relation.

I would REALLY appreciate your help. Thanks.

R. Khan

Date: 01/28/98 at 12:09:42
From: Doctor Loni
Subject: Re: Homework

A relation essentially tells you that for any given value of x you 
will get a value for y. It's like putting a number in a big black box, 
cranking the handle, and getting another number out. 

The textbook definition says that a relation is a set of ordered 
pairs.  To solve the types of problems in your homework you need to 
look at the relation between the x and y (or a and b or whatever 
variable is being used). What is being done to each of the first set 
of numbers (called the domain) which gives you the second set of 
numbers (called the range)? 

For example, in problem number 2 you will notice that each x and y add 
up to 15. Writing it mathematically looks like:

              x + y = 15

Solving for y, the equation for this relation is:

                  y = 15 - x

Equations are usually written in the form y = ... You want what comes 
out of the "black box" to be isolated on one side of the equation.  
In other words, x is what goes in and y is what comes out. Let's try 
putting 10 in for x in our equation. (In other words we are putting 10 
into the box.) When we do that we get 

                  y = 15 - 10 = 5
    
so 5 is what we get out of this box when we put 10 in.

If your variables are not x and y, you want whichever variable is 
associated with the range isolated on one side of the equation. (It is 
called the dependent variable; its value depends on the value of the 
other variable, in this case x.)

In numbers 5-7, the numbers are written in what is called "ordered 
pairs" but if it makes it easier you can write them the same way as 
the first few problems. For instance you can write number 5 like this:

   X    -2    -1     0     1     2
   Y     4     1     0     1     4

You can see here that each y value is the square of the x value (i.e. 
-2 squared is 4, 0 squared is 0, 1 squared is 1, etc.)  Therefore the 
equation for the relation would be:

        y = x^2   (x^2 is a way to type "x squared")

Not all of the problems are obvious, so graphing them can really, 
help.  You can then see if you are dealing with a line or a parabola 
or some other sort of relation. 

I hope this helps.  Let us know if you are still having problems or 
need some extra explanation!

-Doctor Loni,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/