Question

How do you find the domain and range of `y = (x(x-3) )/ (x-4)`?

Answer 1

Domain: `x in RR | x!=4`, in interval notation: `(-oo , 4) uu (4, oo)`
Range : `y in RR` , in interval notation: `(-oo , oo)`

Explanation:

`y = (x(x-3))/(x-4)`

Domain: Denominator is undefined at `0 :. x-4 != 0 or x != 4`

Domain: `x` may be any real number except `4 :. x in RR | x!=4`

In interval notation: `(-oo , 4) uu (4, oo)`

Range : Any real number i.e `y in RR`

In interval notation: `(-oo , oo)`

graph{(x(x-3))/(x-4) [-640, 640, -320, 320]}