What is the domain and range of #y=2^(x-1)+1#?

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Answer 1 · 2017-07-27T13:59:50

Domain: #(-oo, +oo)#
Range: #(1, +oo)#

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

# y# is defined #forall x in RR -># the domain of #y = (-oo, +oo)#

#lim_(x->-oo) y = 1#

#lim_(x->+oo) y = oo#

Hence the range of #y = (1, +oo)#

This can be seen by the graph of #y# below.

graph{2^(x-1)+1 [-7.78, 6.27, -0.74, 6.285]}