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

1 Answer
Apr 22, 2018

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

Explanation:

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

The denominator of y cannot equal 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"

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

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

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

rArry(x+4)=x-2

rArrxy+4y-x+2=0

rArrx(y-1)=-2-4y

rArrx=-(2+4y)/(y-1)

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

rArr"range "y inRR,y!=1

y in(-oo,1)uu(1,oo)
graph{(x-2)/(x+4) [-10, 10, -5, 5]}