What is the domain and range of #y= 1/(x-7) -3#?

1 Answer
Jan 28, 2018

Answer:

#x inRR,x!=7#
#y inRR,y!=-3#

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]}