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# Rational functions watch

1. Find a condition on p such that y=x^2+px/x^2+p takes all values as x varies

I just dont get it I know that x^2+p cannot equal 0 but then have no clue what to do.
2. (Original post by Econowizard)
Find a condition on p such that y=x^2+px/x^2+p takes all values as x varies

I just dont get it I know that x^2+p cannot equal 0 but then have no clue what to do.
If then what does that imply about ?
3. (Original post by Desmos)
If then what does that imply about ?
p greater than minus square root x.... but that isnt the answer
4. (Original post by Econowizard)
Find a condition on p such that y=x^2+px/x^2+p takes all values as x varies
I guess this is ?

If you choose any , you want to be able to find an such that has a solution. But that is equivalent to saying that

has a real solution (i.e. a real choice of ) for any choice of . Can you carry on?
5. (Original post by Econowizard)
p greater than minus square root x.... but that isnt the answer
no no nooooooooooooooooooooooooooooooo ooooooooooooooooooo

first is can x²+p ever equal 0?

if so find the value of x which does so

if not then what is the minimal value of x²+p

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