What is the domain and range of #f(x) = 4 / (x+2)#?

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Answer 1 · 2018-05-16T13:14:58

The domain is #x in (-oo,-2)uu(-2,+oo)#. The range is #y in (-oo,0) uu(0, +oo)#.

The denominator must be #!=0#

#x+2!=0#

Therefore,

#x!=-2#

The domain is #x in (-oo,-2)uu(-2,+oo)#

To find the range, procceed as follow.

Let #y=4/(x+2)#

#=>#, #y(x+2)=4#

#=>#, #yx+2y=4#

#=>#, #yx=4-2y#

#=>#, #x=(4-2y)/y#

The denominator must be #!=0#

#y!=0#

The range is #y in (-oo,0) uu(0, +oo)#

graph{4/(x+2) [-32.48, 32.48, -16.24, 16.24]}