What is the domain and range of # y=3/(x+4)#?

1 Answer
Apr 27, 2017

Answer:

#x inRR,x!=-4#

#y inRR,y!=0#

Explanation:

The denominator of y cannot be zero as this would make y #color(blue)"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 is " x inRR,x!=-4#

#"to find range express function with x as subject"#

#rArry(x+4)=3#

#rArrxy+4y=3#

#rArrxy=3-4y#

#rArrx=(3-4y)/y#

#"the denominator cannot be zero"#

#rArr"range is " y inRR,y!=0#
graph{3/(x+4) [-16.02, 16.02, -8.01, 8.01]}