Hello, macca101!

You did a good job . . . one error.

**Domain**: all

**Intercepts**:

**Sign table** is positive on the intervals:

. . . no
and negative on

is negative on . . . then positive on

**Derivative of ** has fixed points at:

**First derivative test** is found to be a local minimum

and

is found to be a local maximum.

**Sign table of **
The function is found to be decreasing on

and increasing on

**Asymptotes**
Vertical asymptotes are:

and

For horizontal asymptotes, examine: . and

We have: .

Hence, the horizontal asymptote is: . , the x-axis.

There is plenty of information (which *you* found) for sketching the graph.

Code:

:* | *:
: | :
: * | * :
: * | :
: *| * : *
: |* : * *
: | : * *
--------------:-----+-----:---*----------------------
* : | : *
* : | :
* : | : *
* : | :
: | :
*: | :*

I'll let *you* label the intercepts, asymptotes and critical points.