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

1 Answer
Jim G.
Apr 22, 2018

#x inRR,x!=-4,y inRR,y!=1#

Explanation:

#"let " y=(x-2)/(x+4)#

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+4=0rArrx=-4larrcolor(red)"excluded value"#

#rArr"domain "x inRR,x!=-4#

#x in(-oo,-4)uu(-4,oo)larrcolor(blue)"in interval notation"#

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

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

#rArrxy+4y-x+2=0#

#rArrx(y-1)=-2-4y#

#rArrx=-(2+4y)/(y-1)#

#"solve "y-1=0rArry=1larrcolor(red)"excluded value"#

#rArr"range "y inRR,y!=1#

#y in(-oo,1)uu(1,oo)#
graph{(x-2)/(x+4) [-10, 10, -5, 5]}

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