# What is the domain and range of y=2^(x-1)+1?

Jul 27, 2017

Domain: $\left(- \infty , + \infty\right)$
Range: $\left(1 , + \infty\right)$

#### Explanation:

$y = {2}^{x - 1} + 1 = {2}^{x} / 2 + 1$

$y$ is defined $\forall x \in \mathbb{R} \to$ the domain of $y = \left(- \infty , + \infty\right)$

${\lim}_{x \to - \infty} y = 1$

${\lim}_{x \to + \infty} y = \infty$

Hence the range of $y = \left(1 , + \infty\right)$

This can be seen by the graph of $y$ below.

graph{2^(x-1)+1 [-7.78, 6.27, -0.74, 6.285]}