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onegirl
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Determine all horizontal, slant, and vertical asymptotes. For each vertical asymptote, determine whether f(x) > infinity sign of f(x) > negative infinity sign on either side of the asymptote.
 one year ago
 one year ago
onegirl Group Title
Determine all horizontal, slant, and vertical asymptotes. For each vertical asymptote, determine whether f(x) > infinity sign of f(x) > negative infinity sign on either side of the asymptote.
 one year ago
 one year ago

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onegirl Group TitleBest ResponseYou've already chosen the best response.0
f(x) = x^2/4  x^2
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
is it \[\frac{x^2}{4x^2}\]?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
ok so for the vertical asymptotes, set the denominator equal to zero and solve for \(x\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
you get \[4x^2=0\] or \[(2x)(2+x)=0\] and the solutions are \(x=2\) or \(x=2\) those are your vertical asymptotes (there are two of them)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
for the horizontal asymptote, note that the numerator and denominator have the same degree (both are degree 2) so it is the ratio of the leading coefficients
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the leading coefficient of \(x^2\) is 1 and the leading coefficient of \(4x^2\) is \(1\) therefore the horizontal asymptote is \(y=1\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
that is in the case where the degrees are the same. there is no slant asymptote for there to be a slant asymptote , the degree of the numerator would have to be one more than the degree of the denominator
 one year ago
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