How do you graph #f(x)=(3/2)^x-2# and state the domain and range?

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Answer 1 · 2017-12-19T11:30:33

Domain: #(-oo,+oo)#
Range: #(-2,+oo)#

#f(x) = (3/2)^x-2#

#f(x)# is the exponential increasing graph of #y=(3/2)^x# transformed ("shifted") by 2 units negative ("down") on the #y-#axis.

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

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

Consider, #lim_(x->-oo) f(x) =-2#

also, #f(x)# has no finite upper bound.

Hence, the range of #f(x)# is #(-2, +oo)#

We can deduce these results from the graph of #f(x)# below.

graph{(3/2)^x -2 [-10, 10, -5, 5]}