Question

What is the domain and range for `h(x)=6 - 4^x`?

Answer 1

As for `x` there are no limitations.

So the domain is
`-oo < x < +oo`

As for the range :
As `x` gets larger (positive), the function gets more into the negative.
As `x` gets larger (negative), the `4^x`-part will be nearer and nearer to `0`, so the function as a whole will be nearing `6`
In short:
`-oo < h(x)<6`
graph{6-4^x [-22.67, 28.65, -14.27, 11.4]}