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

2 Answers
Apr 22, 2015

Here's my attempt:

y<2 is the range.

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

2-y=2^x

and also,

ln(2-y)=xln2

=> 2-y>0 => y<2

May 21, 2015

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

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

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