Question

How do you graph and find the discontinuities of `y=(3x) /( 4-x^2)`?

Answer 1

For discontinuities you first look at the denominator.

Explanation:

That can be factorised into `(2-x)(2+x)`

So `x=2orx=-2` will make the denominator `=0` and are not allowed.
Also the function will come to look like `-3/(4x)` as the `4` will make less and less difference as `x` grows larger, or:

`lim_(x-> oo)=0and lim_(x-> -oo)=0`
graph{3x/(4-x^2) [-16.02, 16.01, -8.01, 8.01]}