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.