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:

enter image source here

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