# How do you find the domain and range of y=-2^(x)+3?

Apr 21, 2015

Domain is $D = \mathbb{R}$, range is (-oo;3)

The domain of an expresion is the largest subset of $\mathbb{R}$ for which the expresion can be calculated. Possible limitations can be:
To calculate range you have to start from the range of exponential function $y = {2}^{x}$. This is $\left(0 , \infty\right)$
When you multiply such function by (-1) (the minus sign before ${2}^{x}$) the range turns to $\left(- \infty , 0\right)$.
Finally if you add 3 the range also moves, so finally you get (-oo;3)