What is the domain and range of #y = (x + 2) /( x + 5)#?

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Answer 1 · 2018-06-18T12:58:00

The domain is #x in (-oo,-5) uu(-5,+oo)#. The range is #y in (-oo,1)uu(1,+oo)#

The denominator must be #!=0#

Therefore,

#x+5!=0#

#=>#, #x!=-5#

The domain is #x in (-oo,-5) uu(-5,+oo)#

To find the range, proceed as follows :

#y=(x+2)/(x+5)#

#=>#, #y(x+5)=x+2#

#=>#, #yx+5y=x+2#

#=>#, #yx-x=2-5y#

#=>#, #x(y-1)=2-5y#

#=>#, #x=(2-5y)/(y-1)#

The denominator must be #!=0#

Therefore,

#y-1!=0#

#=>#, #y!=1#

The range is #y in (-oo,1)uu(1,+oo)#

graph{(x+2)/(x+5) [-26.77, 13.77, -10.63, 9.65]}