what actually are asymptotes and could you give some examples
maths alevel Watch
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- 13-01-2017 10:33
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- 13-01-2017 13:34
tends to a particular value or
For example; the asymptotes of are and because for those values the function is not defined. If I was to change the denominator into then I still retain the two asymptotes as above but I also have one more which is at as the function is now not defined at that point.
Another example; has asymptotes at so the graph approaches , and , and etc...
Another example; has an asymptote at but this is one of the scenarios where the curve DOES intersect the asymptote (at 1,1) unlike most others which are more common. The function merely has to approach the asymotote, not necessarily avoid intersecting it. So as the function tends to 1 hence why y=1 is the asymptote.
Final example; has an asymptote of because the original function can be represented as so as you have so this is an example of a non-linear asymptote that the original graph approaches.Last edited by RDKGames; 13-01-2017 at 13:50.
- 13-01-2017 13:47
It's usually shown graphically with dashed lines like this
RDKGames has provided some good examples and explanations above which are probably of more use