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

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Answer 1 · 2018-04-27T13:27:28

The domain is #x in RR#. The range is #y in (0, +oo)#

The function is

#y=2^(-x)=1/2^x#

#lim_(x->-oo)y=lim_(x->-oo)1/2^x=oo#

#lim_(x->+oo)y=lim_(x->+oo)1/2^x=0#

#AA x in RR, 1/2^x>0#

The domain of #y# is #x in RR#

#2^x=1/y#

#ln(2^x)=ln(1/y)#

#xln2=ln(1/y)=ln1-lny=-lny#

#x=-1/ln2lny#

Therefore,

#y in (0, +oo)#

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

graph{2^(-x) [-10.81, 14.5, -2.89, 9.77]}