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

1 Answer
Jan 29, 2018

Answer:

#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]}