How do you determine the domain, range and horizontal asymptote of each exponential function # f(x) = 1 - 2^[(-x/3)]#?

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Answer 1 · 2017-11-18T19:26:27

See below.

There are no restrictions on #x# so domain is:

#{x in RR}#

For positive #x# we have:

#y=1-1/2^(x/3)#

as #x->oocolor(white)(8888)1-1/2^(x/3)->1color(white)(88)# ( horizontal asymptote )

For negative #x# we have:

#y=1-2^(x/3)#

as #x->-oocolor(white)(8888)1-2^(-x/3)->-oo#

So range is:

#{y in RR : -oo < y < 1 }#

Graph:

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