asymptote question

[tram]

what would you say the asymptotes for the graph

(x^3 - 1)/ x

are?

(soz for the lack of latex)

[Souljette_93]

Wouldn't it be and ?

[Martoman]

I usually work with limits.



as x gets very big or very big negatively the 1/x fraction becomes stupidly close to 0 as the 1/x graph has an asymptote there. The other reasoning if you don't like looking at it graphically is that so small in fact that its negligeable. so y approaches x^2 as x is very big in the negative or positive direction. The other asymptote to obserive is if x= 0, as that would mean the 1/x term is 1/0 ie undefined.

[tram]

yeah, see my think was EXACTLY what both of you guys said, only i had a srsly lengthy discission with my friends about whether or not y= -1/x was also an asymptote. I said that the asymptote x=0 covered this but they insisted that it was necessary. Opinions?

[brightsky]

yeah, see my think was EXACTLY what both of you guys said, only i had a srsly lengthy discission with my friends about whether or not y= -1/x was also an asymptote. I said that the asymptote x=0 covered this but they insisted that it was necessary. Opinions?

Hmm..I think it's clear enough from the graph that y = -1/x isn't an asymptote. Also, it doesn't correlate to any of the usual techniques used to find asymptotes. Are you able to provide the reasoning behind their answer?

[tram]

well, it had to do with the fact that you were effectively adding ordinates and thus as x approaches 0, then obvsiously x^2 approaches zero, and that means that the graph is apporaching whatever -1/x is => it is an asymptote.

[brightsky]

well, it had to do with the fact that you were effectively adding ordinates and thus as x approaches 0, then obvsiously x^2 approaches zero, and that means that the graph is apporaching whatever -1/x is => it is an asymptote.

Why let x tend to zero?

[supernatural]

i think it would be and

the same question was in the mav 2010 trial. thats what the answers say as well.

because when x -> ∞  f(x) ->    but doesn't touch it, meaning its an asymptote
and x cannot be zero too, so that's an asymptote as well

I said that the asymptote x=0 covered this

i think so as well. when x-> 0 [from the left or right]  f(x)->

and what are the asymptotes for ?  x = 0

so x=0 covers this i guess