C3 curve sketching (asymptotes) Watch

The Guvnor
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Report Thread starter 12 years ago
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Does anyone have a good guide or link to one for curve sketching. I know it crosses axes when x&y=o, differentiate for the turning points, its the asymptote stuff I really don't get.
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James
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Consider:
1. Where does it cross the axes?
2. What happens to y as x tends to infinity/negative infinity?
3. Where are the turning points?
4. Where are the asymptotes?

Asymptotes occur in places where the function cannot be evaluated. For example, if y=(x-5)/[(x+4)(x-2)] then there will be vertical asymptotes at x=2 and x=-4. At these x-ordinates, no value for y can be calculated.

Horizontal asymptotes occur when a function converges as x tends to +- infinity. For example, the function y=e^-x converges to 0 as x increases. This is shown by an asymptote along the line y=0.

The graph y=1/x has a vertical asymptote for the first reason discussed, and a horizontal one for the second reason.

Hope this helps.
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Kolya
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Report 12 years ago
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It is important that you learn curve sketching as it is a useful skill.

From the point of exams though, I would get yourself a graphical calculator just incase to get best mark you can...
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