Question

What is the domain and range of `y=3/(x+4)`?

Answer 1

`x inRR,x!=-4`

`y inRR,y!=0`

Explanation:

The denominator of y cannot be zero as this would make y `color(blue)"undefined".` Equating the denominator to zero and solving gives the value that x cannot be.

`"solve " x+4=0rArrx=-4larrcolor(red)" excluded value"`

`rArr"domain is " x inRR,x!=-4`

`"to find range express function with x as subject"`

`rArry(x+4)=3`

`rArrxy+4y=3`

`rArrxy=3-4y`

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

`"the denominator cannot be zero"`

`rArr"range is " y inRR,y!=0`
graph{3/(x+4) [-16.02, 16.02, -8.01, 8.01]}