# Thread: Functions and Curve Sketching

1. ## Functions and Curve Sketching

A curve is given by the equation $y = \frac{ax^2 + bx + c}{dx^2 + ex + f}$ . The equations of the asymptotes to the curve are x = 1, x = 3 and y = 1. The curve passes through the points (2,0) and the origin..

I figured how to find d, e and f by taking the x asymptotes and make them = 0 ...getting $\frac{ax^2 + bx + c}{(x-1)(x-3)}$ I can't seem to figure out how to find a b and c though..any help would be greatly appreciated.

2. Originally Posted by kleyzam
A curve is given by the equation $y = \frac{ax^2 + bx + c}{dx^2 + ex + f}$ . The equations of the asymptotes to the curve are x = 1, x = 3 and y = 1. The curve passes through the points (2,0) and the origin..

I figured how to find d, e and f by taking the x asymptotes and make them = 0 ...getting $\frac{ax^2 + bx + c}{(x-1)(x-3)}$ I can't seem to figure out how to find a b and c though..any help would be greatly appreciated.

2. If $\lim_{|x|\rightarrow \infty}\left(\dfrac{ax^2 + bx}{x^2-4x+3} \right)=1~\implies~ a = 1$
3. If $f(2) = 0$ then $2^2+2b=0~\implies~b = -2$
4. Therefore $f(x)=\dfrac{x^2 -2x}{x^2-4x+3}$