Question

How do you find the domain and range of `1/(x+4)`?

Answer 1

`x inRR,x!=-4, y inRR.y!=0`

Explanation:

`"let "y=1/(x+4)`

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

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

`(-oo,-4)uu(-4,oo)larrcolor(blue)"in interval notation"`

`"to find the range, rearrange making x the subject"`

`y(x+4)=1`

`xy+4y=1`

`xy=1-4y`

`x=(1-4y)/y`

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

`"range "y inRR,y!=0`

`(-oo,0)uu(0,oo)`
graph{1/(x+4) [-10, 10, -5, 5]}