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Find the domain and range of the function. `f(x,y) = x/y`

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user9055008 | eNotes Newbie

Posted May 23, 2013 at 12:14 PM via web

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Find the domain and range of the function.

`f(x,y) = x/y`

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oldnick | Valedictorian

Posted May 24, 2013 at 4:11 AM (Answer #1)

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`f(x;y)=x/y`

it's defined  `D=<<AA x in RR >> xx<< AA y in RR | y!=0 >>`

We se function is not limited  for, x wit a finte value and y too much close to zero on the left or right the function has greater module values :

`lim_(y->0^+) f(x,y)= -oo`     `lim_(y->0^-) f(x;y)= +oo`

On the other side, for y with a finte value , and x approaching to zero:

`lim_(x->0) f(xy)=0`

So the range of `f(x,y)`  is `(-oo;+oo)`

This graph is projection f(x;y) wich every colored line stands for a fixed x value.

It's show function graph is a hiperbolyc parapholoid  

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pramodpandey | College Teacher | Valedictorian

Posted May 24, 2013 at 4:18 PM (Answer #2)

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f(x,y)=x/y

domain of this function is R x (R-{0})

That is function is defind for all real nomber in plane R xR except y=0

Range  is Real number R.

 

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