Sketch two periods of the function y = 2 tan 2x
- Thread starter mrsgigo
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If you understand the basic function, these do not have to be painful.
y = tan(x) does what? It has vertical asymptotes everywhere cos(x) = 0. Draw a few of those. tan(x) = 1 everywhere sin(x) = cos(x). This is at pi/4 and every pi after that. Draw a few of those. It is zero everywhere sin(x) = 0. That's x = 0 and every pi after that. Draw a few of those. You should be seeing the shape of the thing. Sketch a few periods.
y = 2tan(x) This is just a little vertical stretching. Start with the graph previously described. Erase whatever you labled (pi/4,1) and relable it (pi/4,2). You're almost done. Relable a few more things and move on.
y = 2tan(2x) This is just a little horizontal compression. Start with the graph previously described. Erase whatever you labled (pi/4,2) and relable it (pi/8,2). You're almost done. Relable a few more things and move on.
y = tan(x) does what? It has vertical asymptotes everywhere cos(x) = 0. Draw a few of those. tan(x) = 1 everywhere sin(x) = cos(x). This is at pi/4 and every pi after that. Draw a few of those. It is zero everywhere sin(x) = 0. That's x = 0 and every pi after that. Draw a few of those. You should be seeing the shape of the thing. Sketch a few periods.
y = 2tan(x) This is just a little vertical stretching. Start with the graph previously described. Erase whatever you labled (pi/4,1) and relable it (pi/4,2). You're almost done. Relable a few more things and move on.
y = 2tan(2x) This is just a little horizontal compression. Start with the graph previously described. Erase whatever you labled (pi/4,2) and relable it (pi/8,2). You're almost done. Relable a few more things and move on.
D
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You ought to have a "graphing calculator" - use it.
If you don't - download one of many free graphing utilities available (e.g. fngraph, graph, etc.). These are very useful and robust.
If you don't - download one of many free graphing utilities available (e.g. fngraph, graph, etc.). These are very useful and robust.
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This should have been caught years ago, back in algebra. I'm surprised nobody pulled you aside and tried to help you back then. :shock:mrsgigo said:
Unfortunately, your lack of background (working with the x,y-plane; graphing linear, quadratic, etc, curves; understanding functions and their domains and ranges; etc, etc) would require weeks or months of intensive hands-on instruction to remedy. Obviously, this isn't something that can be provided within this environment. Sorry!
Please consider hiring a tutor, local to your area, and meeting with him a few hours a week (daily would be best). With luck and a fair amount of effort, you may be able to get caught up on only a month or two.
My best wishes to you in your studies!
Eliz.