What is the domain and range of y= 1/(x-7) -3y=1x−7−3?
1 Answer
Jan 28, 2018
Explanation:
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-7=0rArrx=7larrcolor(red)"excluded value"
rArr"domain is "x inRR,x!=7
(-oo,-7)uu(-7,+oo)larrcolor(blue)"in interval notation"
"divide numerator/denominator of "1/(x-7)" by x"
y=(1/x)/(x/x-7/x)-3=(1/x)/(1-7/x)-3
"as "xto+-oo,yto0/(1-0)-3
rArry=-3larrcolor(red)"excluded value"
"range is "y inRR,y!=-3
(-oo,-3)uu(-3,+oo)larrcolor(blue)"in interval notation"
graph{1/(x-7)-3 [-10, 10, -5, 5]}
