Here is a rational function:

$\displaystyle f(x)= \frac {3x^2}{4-x^2} $

Find:

domain: (- infinity, infinity)

Range: (- infinity, -2)U(-2,2)U(2, infinity)

x-intercept:

y-intercept: none

roots:

Asymptotes:

For y-intercept:

Let x=0

$\displaystyle f(0)= \frac {3(0)^2}{4-0^2} $

$\displaystyle f(x)= 0 so, Y=0 (No Y-intercept)$

For x-intercept:

$\displaystyle f(x)= \frac {3x^2}{4-x^2}=0 $

I factor the denominator:

$\displaystyle f(x)= \frac {3x^2}{(x-2)(x+2)} $

What is next ? >.<