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Should you check the value of a function on its asymptote to get a good idea of how its graph should look?
Wiki User
∙ 7y ago
The asymptote is a line where the function is not valid - i.e the function does not cross this line, in fact it does not even reach this line, so you cannot check the value of the function on it's asymptote.
However, to get an idea of the function you should look at it's behavior as it approaches each side of the asymptote.
Wiki User
∙ 7y ago
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To get a good idea of how its graph should look should you check the value of a function on its asymptote?
FALSE
Is it true that you should always check a function's values on both sides of its asymptote?
It is often a good idea. But consider this: it may not have a value on the wrong side of the asymptote. Try graphing y = 1/x.
How do you find asymptotes of any function?
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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