Is there a secret to finding assymptotes quickly? It always seems to take a while for me to work out where they are! As you can tell, I'm terrible with graphing functions!
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- Thread Starter
- 10-08-2004 21:55
- 10-08-2004 22:14
Asymptotes are lines on the graph that the function tends towards but never quite reaches.
Usually x, or y will tend to infinity as y, or x tends to some other value.
e.g. y = 1/x
as x-> 0, y ->∞
So, the y-axis (x=0) is one asymptote
y = 1/(1-x)
as x->1, y ->∞
So, the line x=1 is an asymptote.
y = 1+1/x
as x->∞, y ->1
So, y=1 is an asymptote.
In the simple cases, look for denominators that can take a zero value.
It's not always vertical, or horizontal, lines that are asymptotes. For example in the function
x² - y² = 1
The asymptotes are not at all obvious - they are the lines y = ±x.
This is a case where it's better to draw the curve and see what it looks like.
Hmm, there's not too much help here. Hopefully some of the other lads can give some more advice