Question

What is the domain and range of `y = (3(x-2))/x`?

Answer 1

`x inRR,x!=0,y inRR,y!=3`

Explanation:

The denominator of y cannot be zero as this would make y undefined.

`rArrx=0larrcolor(red)" excluded value"`

`"domain is " x inRR,x!=0`

To find any excluded value in the range, rearrange making x the subject.

`rArrxy=3x-6larrcolor(blue)" cross-multiply"`

`rArrxy-3x=-6larr" collect terms in x"`

`rArrx(y-3)=-6larr" common factor of x"`

`rArrx=-6/(y-3)`

`"the denominator cannot equal zero"`

`y-3=0rArry=3larrcolor(red)" excluded value"`

`"range is " y inRR,y!=3`