Originally Posted by
skeeter $\displaystyle f(x) = \frac{3x(x-2)}{(x+2)(x-2)}$
$\displaystyle f(0) = 0$ ... y-intercept
$\displaystyle f(x) = 0$ at $\displaystyle x = 0$ ... x-intercept
vertical asymptote, $\displaystyle x = -2$ ... $\displaystyle (x+2)$ in the denominator
removable discontinuity (a "hole") at $\displaystyle x = 2$ ... $\displaystyle (x-2)$ in both numerator and denominator
horizontal asymptote at $\displaystyle y = 3$ ... degree of the numerator = degree of the denominator ... ratio of the leading coefficients in the numerator and denominator gives you the value of the horizontal asymptote.