Question

What is the domain and range of `y = (x-3)/(x+11)`?

Answer 1

`x inRR,x!=-11`
`y inRR,y!=1`

Explanation:

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

`"solve "x+11=0rArrx=-11larrcolor(red)"excluded value"`

`rArr"domain is "x inRR,x!=-11`

`(-oo,-11)uu(-11,+oo)larrcolor(blue)"in interval notation"`

`"divide terms on numerator/denominator by x"`

`y=(x/x-3/x)/(x/x+11/x)=(1-3/x)/(1+11/x)`

`"as "xto+-oo,yto(1-0)/(1+0)`

`rArry=1larrcolor(red)"excluded value"`

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

`(-oo,1)uu(1,+oo)larrcolor(blue)"in interval notation"`
graph{(x-3)/(x+11) [-20, 20, -10, 10]}