Question 1074629
<pre><b>
Here's the graph of {{{y}}}{{{""=""}}}{{{5/x}}}.

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10,5/x) )}}} 

It has asymptotes which are the x-axis (y=0) and the y-axis (x=0)
and we want to move the graph so that it has x=-3 and y=-2, which
are these green lines, as asympotes instead.

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10,5/x),
green(line(-3,-15,-3,15),line(-15,-2,15,-2))

 )}}} 

So as you see we want to shift the graph 3 units left and 2
units down.

So we replace x by (x+3) and add -2 to the right side:

 {{{y}}}{{{""=""}}}{{{5/(x+3)-2}}}

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10,15,16,17,18,19,(5/x)*sqrt(sin(9x))/sqrt(sin(9x))),graph(400,400,-10,10,-10,10,5/(x+3)-2),
green(line(-3,-15,-3,15),line(-15,-2,15,-2)))}}}

So the new graph with equation {{{y}}}{{{""=""}}}{{{5/(x+3)-2}}} has the
green line as asymptotes.  The original graph is dotted in
light blue.

If you like you can combine the terms on the right side:

 {{{y}}}{{{""=""}}}{{{5/(x+3)-(2(x+3))/(x+3)}}}

 {{{y}}}{{{""=""}}}{{{5/(x+3)-(2x+6)/(x+3)}}}

 {{{y}}}{{{""=""}}}{{{(5-2x-6)/(x+3)}}}

 {{{y}}}{{{""=""}}}{{{(-2x-1)/(x+3)}}}

 {{{y}}}{{{""=""}}}{{{(-(2x+1))/(x+3)}}}

 {{{y}}}{{{""=""}}}{{{-(2x+1)/(x+3)}}}

But that probably isn't necessary.

Edwin</pre></b>