How do you find the domain and range of #f(x) = 7/(x+3)#?

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Answer 1 · 2018-05-01T09:20:37

The domain is #x in (-oo, -3)uu (-3, +oo)#.
The range is #y in (-oo, 0) uu (0, +oo)#

Let #y=(7)/(x+3)#

The denominator is #!=0#

Therefore,

#x+3!=0#

#x!=-3#

The domain is #x in (-oo, -3)uu (-3, +oo)#

Also,

#y(x+3)=7#

#yx+3y=7#

#yx=4-3y#

#x=(4-3y)/(y)#

The denominator is #!=0#

Therefore

#y!=0#

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

graph{(y-((7)/(x+3)))(y-0)=0 [-36.53, 36.52, -18.28, 18.27]}