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Definition: If lim x->a^(+/-) f(x) = +/- Infinity, then we say x=a is a vertical asymptote.
If lim x->+/- Infinity f(x) = a, then we say f(x) have a horizontal asymptote at a
If l(x) is a linear function such that lim x->+/- Infinity f(x)-l(x) = 0, then we say l(x) is a slanted asymptote.
As you might notice, there is no generic method of finding asymptotes. Rational functions are really nice, and the non-permissible values are likely vertical asymptotes.
Horizontal asymptotes should be easiest to approach, simply take limit at +/- Infinity
Vertical Asymptote just find non-permissible values, and take limits towards it to check
Slanted, most likely is educated guesses.
If you get f(x) = some infinite sum, there is no reason why we should be able to to find an asymptote of it with out simplify and comparison etc.
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What do the asymptotes represent when you graph the tangent function?
When you graph a tangent function, the asymptotes represent x values 90 and 270.
Is it possible for graph of function to cross the horizontal assymptotes?
When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.
How many non-verticle asymptotes can a rational function have?
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
How many asymptotes can a bounded function have?
I believe the maximum would be two - one when the independent variable tends toward minus infinity, and one when it tends toward plus infinity. Unbounded functions can have lots of asymptotes; for example the periodic tangent function.
