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

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Answer 1 · 2015-04-22T19:27:46

Here's my attempt:

$y < 2$ $y<2$ is the range.

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

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

and also,

$ln (2 - y) = x ln 2$ $ln(2-y)=xln2$

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

Answer 2 · 2015-05-21T22:36:36

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

I'd start from a known fact that $a^{x} > 0$ $a^x>0$ for all $a > 0$ $a>0$ and $x in RR$ .
So:

$2^x>0$
$-2^x<0$
$-2^x+2<2$
$y<2$
$y in (-infty;2)$

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