# How do I find the range of the function y=-2^x+2

How do I find the range of the function $y=-{2}^{x}+2$?
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Houston Ellis
Here's my attempt:
y<2 is the range.
$y=-{2}^{x}+2$ Can also be written as
$2-y={2}^{x}$
and also,
$\mathrm{ln}\left(2-y\right)=x\mathrm{ln}2$
$⇒2-y>0⇒y<2$
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tun1ju2k1ki
The range of $y=-{2}^{x}+2$ is $\left(-\mathrm{\infty };2\right)$
I'd start from a known fact that ${a}^{x}>0$ for all a>0 and $x\in \mathbb{R}$
So:
${2}^{x}>0$
$-{2}^{x}<0$
$-{2}^{x}+2<2$
y<2
$y\in \left(-\mathrm{\infty };2\right)$