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

1 Answer
Jim G.
Apr 27, 2017

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]}

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