What is the domain and range of $y= 1/2(2)^x$ ?

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Answer 1 · 2016-01-24T12:47:19

The domain is $(-oo, oo)$ . The range is $(0, oo)$ .

$2^x$ is well defined for any Real number $x$ . Hence the function $f(x) = 1/2 (2)^x$ is also well defined for any $x in (-oo, oo)$ .

It is also continuous and strictly monotonically increasing.

As $x->-oo$ we find $2^x -> 0_+$

As $x->oo$ we find $2^x -> oo$

So the range is $(0, oo)$

graph{2^x/2 [-10.12, 9.88, -1.52, 8.48]}

What is the domain and range of y= 1/2(2)^xy= 1/2(2)^x?