Question

How do you find domain and range for `f(x)=(x-2)/(x+4)`?

Answer 1

`x inRR,x!=-4,y inRR,y!=1`

Explanation:

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

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

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

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

`"let "y=(x-2)/(x+4)`

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

`y(x+4)=x-2`

`xy+4y=x-2`

`xy-x=-2-4y`

`x(y-1)=-2-4y`

`x=(-2-4y)/(y-1)`

`"solve "y-1=0rArry=1larrcolor(red)"excluded value"`

`"range is "y inRR,y!=1`

`"or "(-oo,1)uu(1,oo)`
graph{(x-2)/(x+4) [-10, 10, -5, 5]}