How do you graph #f(x)=2^x+1# and state the domain and range?

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Answer 1 · 2017-08-30T12:09:57

Domain: #(-oo, +oo)# Range: #(1, +oo)#
Graph: See below

#f(x) = 2^x+1#

The graph of #f(x)# is the standard graph of #2^x# transformed ("shifted") one unit positive ("up") on the #y-#axis.

#f(x)# is defined #forall x in RR#

#:.# the domain of #f(x)# is #(-oo, +oo)#

Consider:

(i) #lim_(x->-oo) f(x) = 0+1 =1#

(ii) #f(x)# has no finite upper bound

Hence, the range of #f(x)# is #(1, +oo)#

The domain and range of #f(x)# may be inferred from its graph below.

graph{2^x+1 [-12.34, 7.655, -1.88, 8.12]}