Hello, vvc531!
This is a very messy problem . . .
Suppose that a rational function approaches the lines and asymptotically.
Sketch a graph of this function and write an equation that describes this function.
The vertical asymptote is simple: we need in the denominator.
Now we want a function: . .which approaches . .as
Hence, the numerator must be a quadratic.
We want: .
Long division: .
Hence: .
. . . . . .
. . . . . .
Let and one function is: .
And the graph looks something like this:
Code:
. *. |
.* . |
.* *. |
. * . |
. * * . |
. * . |
. . |
. . |
. |
. . |
. . |
. * . |
. * * .3
. * .
.* | *.
. | *. 3
------------------.*------+-------.------
-2 | *.
. | .
. |
Um, my scale is off.
The intercepts should be: .(0, 0) and (1, 0)
I hope you can modify the graph.