Question

How do you find the domain and range of `y=(-4x-3)/(x-2)`?

Answer 1

`x inRR,x!=2`
`y inRR,y!=-4`

Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

`"solve " x-2=0rArrx=2larrcolor(red)" excluded value"`

`"domain is " x inRR,x!=2`

`"Rearrange the function and make x the subject"`

`rArry(x-2)=-4x-3`

`rArrxy-2y=-4x-3`

`rArrxy+4x=2y-3`

`rArrx(y+4)=2y-3`

`rArrx=(2y-3)/(y+4)`

Again the denominator cannot be zero.

`"solve " y+4=0rArry=-4larrcolor(red)"excluded value"`

`"range is " y inRR,y!=-4`