# What is the domain and range of  y=-2^(x)+3 ?

The domain is $R$ and the range is
$y = - {2}^{x} + 3 \implies {2}^{x} = 3 - y \implies 3 - y > 0 \implies 3 > y$
hence the range is $\left(- \infty , + 3\right]$