Answer:
We must write an equationcthat is a translation of
[tex]y = \frac{2}{x} [/tex]
An that has asymptote of y=3 and x=8.
First, let convert y=2/x into its parent function.
which is
[tex] y = \frac{1}{x} [/tex]
If we multiply the fraction by 2, we get 2/x so our transformed equation is
[tex]y = 2( \frac{1}{x} )[/tex]
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.
[tex]y = \frac{2}{x - 8} [/tex]
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
[tex] \frac{2}{x - 8} [/tex]
We have
[tex] \frac{2x}{x - 8} [/tex]
Now, the leading coeefricent must equal 3 sk we shift 2x to the left x units.
[tex] \frac{3x}{x - 8} [/tex]
Because 3/1=3 so our equation is
[tex] \frac{3x}{x - 8} [/tex]
