# Math Help - plz help with asymptotes and limits

1. ## plz help with asymptotes and limits

Explain what each of the following mathematical statement mean in regard to the graph of f(x).
(1)f(2)=0
(2)lim x->0 f(x)=-infinity
(3) lim x->3+ f(x) = - infinity
(4)lim x->3- f(x)=infinity
(5) lim x->+/- infinity f(x)=0

(b)using our explanation from part(a),sketch the graph of this function.use dotted lines for any asymptotes
(c)find a formua for function f(x)that satisfies the conditions stated in part(a).briefly explain how you determined this function

2. Originally Posted by gracy
Explain what each of the following mathematical statement mean in regard to the graph of f(x).
(1)f(2)=0
(2)lim x->0 f(x)=-infinity
(3) lim x->3+ f(x) = - infinity
(4)lim x->3- f(x)=infinity
(5) lim x->+/- infinity f(x)=0

(b)using our explanation from part(a),sketch the graph of this function.use dotted lines for any asymptotes
(c)find a formua for function f(x)that satisfies the conditions stated in part(a).briefly explain how you determined this function
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:
$f(x)=\frac{x-2}{-x^2(x-3)}$

I've attached a diagram of this function.

EB