OK Here we go....

To Sketch the graph of

1. Find the domain.

The denominator is 0 when so the domain of is all of except for

2. Is the function odd or even.

as is not equal to is neither odd or even

3. The intercepts

The x intercept occurs when

The y intercept occurs at

4. Construct a sign table

Having constructed a sign table (don't know how to create it in LATEX) but gives me the following information to help in the sketching of the graph.

is positive on the interval and negative on

5. The Derivative of

has two fixed points at and

As and the fixed points are located at

After applying the first derivative test is found to be a local minimum and is found to be a local maximum.

Also after constructing the sign table of the function is found to be decreasing on and increasing on

6. Asymptotes

As the denominator is 0 when then the lines and are vertical asymptotes

Now here is the question(s)

1 Is all the above correct ?

2 Does the graph have a horizontal asymptote ?

3 Is there enough information the sketch the graph? (I've had a go but I am unable to reproduce my result here.)

Thanks