How do you find the domain and range of #1/(x+4)#?

1 Answer
Jun 16, 2018

Answer:

#x inRR,x!=-4, y inRR.y!=0#

Explanation:

#"let "y=1/(x+4)#

#"the denominator of y cannot be 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"#

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

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

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

#y(x+4)=1#

#xy+4y=1#

#xy=1-4y#

#x=(1-4y)/y#

#y=0larrcolor(red)"excluded value"#

#"range "y inRR,y!=0#

#(-oo,0)uu(0,oo)#
graph{1/(x+4) [-10, 10, -5, 5]}