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/
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