How do you find the domain and range of f(x)=(x-2)/(x+4) ?
1 Answer
Apr 22, 2018
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]}