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

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Answer 1 · 2015-04-22T19:27:46

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#

Answer 2 · 2015-05-21T22:36:36

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)#