# plz help with asymptotes and limits

• Oct 24th 2006, 08:57 PM
gracy
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
• Oct 25th 2006, 01:50 AM
earboth
Quote:

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