Hi,

(1) f has a zero at x = 2, so the graph intersect the x-axis at (2,0).

(2) f is not defined for x² = 0, because the infinity is not a real value. The graph is only going downward when you approach x = 0, never mind from which side you come. to avoid a change of sign you have to use x² instead of x.

(3) and (4) f is not defined for x = 3. The graph has a asymptote perpendicular to the x-axis at x = 3. At x = 3 is a pole (that's the word used in German. I don't know the corresponding word in English) with change of sign.

(4) the x-axis is horizontal asymptote.

Now you can construct the function.

It looks like rational function with numerator (x-2) (at least) and

denominator (-x^2)(x-3) (at least). So you get:

I've attached a diagram of this function.

EB