Date: 07/24/2002 at 19:35:02 From: Kartik Trehan Subject: Graphing Peculiarity Suppose we have to graph the function y = (x^2 - 4)/(x + 2) Everything seems fine; there is a hole at -2, etc. But what if we move the x+2 to the other side so that (x + 2)y = x^2 - 4. Then when we plug in -2 the equation becomes 0=0, and that doesn't seem to have a graph. What's happening? I couldn't graph it and no online graphing calculators could help me. Either my brain has turned against me or there is some simple explanation for this. Thanks a lot.
Date: 07/25/2002 at 13:40:13 From: Doctor Peterson Subject: Re: Graphing Peculiarity Hi, Kartik. The computers have turned against you. This does have a graph, but it may take a human brain to recognize it! The graph of an equation is a graph of THAT PARTICULAR equation, not necessarily of any equation you can change it to. In this case, you have multiplied the equation by x+2; when x = -2, that means you have multiplied by 0 and the new equation is not equivalent to the original. The graphs will be the same everywhere except at x = -2. You found that when you put x = -2 into the new equation, it becomes 0y = 0; that means that it is true for ALL y! So its graph, rather than having a hole at (-2,-4), consists of the vertical line x = -2 together with the line y = x-2. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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