What is the domain and range of y = (x-3)/(x+11)y=x−3x+11?
1 Answer
Jan 29, 2018
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]}
