How do I find the range of the function $y=-{2}^{x}+2$?

dripcima24
2022-09-07
Answered

How do I find the range of the function $y=-{2}^{x}+2$?

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Houston Ellis

Answered 2022-09-08
Author has **4** answers

Here's my attempt:

y<2 is the range.

$y=-{2}^{x}+2$ Can also be written as

$2-y={2}^{x}$

and also,

$\mathrm{ln}(2-y)=x\mathrm{ln}2$

$\Rightarrow 2-y>0\Rightarrow y<2$

y<2 is the range.

$y=-{2}^{x}+2$ Can also be written as

$2-y={2}^{x}$

and also,

$\mathrm{ln}(2-y)=x\mathrm{ln}2$

$\Rightarrow 2-y>0\Rightarrow y<2$

tun1ju2k1ki

Answered 2022-09-09
Author has **2** answers

The range of $y=-{2}^{x}+2$ is $(-\mathrm{\infty};2)$

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

$y\in (-\mathrm{\infty};2)$

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

$y\in (-\mathrm{\infty};2)$

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