How do you find the domain and range of #y=(-4x-3)/(x-2)#?

1 Answer
Apr 10, 2017

Answer:

#x inRR,x!=2#
#y inRR,y!=-4#

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-2=0rArrx=2larrcolor(red)" excluded value"#

#"domain is " x inRR,x!=2#

#"Rearrange the function and make x the subject"#

#rArry(x-2)=-4x-3#

#rArrxy-2y=-4x-3#

#rArrxy+4x=2y-3#

#rArrx(y+4)=2y-3#

#rArrx=(2y-3)/(y+4)#

Again the denominator cannot be zero.

#"solve " y+4=0rArry=-4larrcolor(red)"excluded value"#

#"range is " y inRR,y!=-4#