Question

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

Answer 1

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

Explanation:

`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]}