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

May 28, 2015

As for $x$ there are no limitations.

So the domain is
$- \infty < x < + \infty$

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:
$- \infty < h \left(x\right) < 6$
graph{6-4^x [-22.67, 28.65, -14.27, 11.4]}