Question

PLEASE HELPP!!!!! Write an equation for the translation of y=2/x that has asymptotes x=8 and y=3

Answer 1

We must write an equationcthat is a translation of

`y = (2)/(x)`

An that has asymptote of y=3 and x=8.

First, let convert y=2/x into its parent function.

which is

`y = (1)/(x)`

If we multiply the fraction by 2, we get 2/x so our transformed equation is

`y = 2( (1)/(x) )`

Right now, we have a asymptoe at x=0 a y=0.

I'll provide you a graph of y=2/x or 2(1/x)

That is the first graph shown,

we have asymptote at x=0 and y=0,

we need a asymptote at x=8, to do that. we just subtract 8 from x.

`y = (2)/(x - 8)`

Now, we I'll give you a graph of 2(1/x-8) or 2/x-8.

Here we have a asymptote at x=8 but we still have a y=0 asymptote. In order for us to a asymptote of y=3,

The numerator and denomiator must be the same degree

So instead of

`(2)/(x - 8)`

We have

`(2x)/(x - 8)`

Now, the leading coeefricent must equal 3 sk we shift 2x to the left x units.

`(3x)/(x - 8)`

Because 3/1=3 so our equation is

`(3x)/(x - 8)`