Square Root Functions and TransformationsDate: 09/07/2009 at 02:33:59 From: Jon Subject: square root functions and transformations How can we tell by looking at a graph if a square root function is being horizontally compressed or vertically stretched? For example, y = 2 sqrt(x) is being vertically stretched when graphed, but y = sqrt(2x) is being horizontally compressed. I'm confused because they both graphically look like they are being horizontally compressed or vertically stretched. However, my textbook makes a distinction for both cases. Ultimately, I would like to know how to tell the difference by merely looking at a graph. Date: 09/07/2009 at 05:34:31 From: Doctor Ali Subject: Re: square root functions and transformations Hi Jon! Thanks for writing to Dr. Math. You asked a very nice question. >How can we tell by looking at a graph if a square root function is >being horizontally compressed or vertically stretched? The answer is, we can't! Note that in the example you gave, we can write y = Sqrt(2x) as y = Sqrt(2) Sqrt(x) ~= 1.4142 Sqrt(x) So, if we just have the graph, is it horizontally compressed by 1/2 or vertically stretched by 1.4142? We can't tell. Does that make sense? Please write back if you still have any difficulties. - Doctor Ali, The Math Forum http://mathforum.org/dr.math/ Date: 09/07/2009 at 12:45:37 From: Jon Subject: Thank you (square root functions and transformations) Thank you very much for the quick response. I really do appreciate it.. Date: 09/10/2009 at 10:27:34 From: Doctor Peterson Subject: Re: square root functions and transformations Hi, Jon. It may be important to point out that not all functions behave like the square root. In general, horizontal compression and vertical stretch are NOT equivalent. (Try doing the same thing with a general linear function, y=ax+b.) In the case of the square root, it happens that we can describe the same transformation either way, making it an arbitrary choice, but that is not usually true. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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