What is the domain and range of y=5/(x-1)?

1 Answer
Mar 5, 2018

x inRR,x!=1
y inRR,y!=0

Explanation:

"the denominator of y cannot equal zero as this would "
"make y undefined. Equating the denominator to zero"
"and solving gives the value that x cannot be"

"solve "x-1=0rArrx=1larrcolor(red)"excluded value"

rArr"domain is "x inRR,x!=1

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

rArry(x-1)=5

rArrxy-y=5

rArrxy=5+y

rArrx=(5+y)/y

rArry=0larrcolor(red)"excluded value"

rArr"range is "y inRR,y!=0
graph{5/(x-1) [-10, 10, -5, 5]}