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

Jan 24, 2016

The domain is $\left(- \infty , \infty\right)$. The range is $\left(0 , \infty\right)$.

#### Explanation:

${2}^{x}$ is well defined for any Real number $x$. Hence the function $f \left(x\right) = \frac{1}{2} {\left(2\right)}^{x}$ is also well defined for any $x \in \left(- \infty , \infty\right)$.

It is also continuous and strictly monotonically increasing.

As $x \to - \infty$ we find ${2}^{x} \to {0}_{+}$

As $x \to \infty$ we find ${2}^{x} \to \infty$

So the range is $\left(0 , \infty\right)$

graph{2^x/2 [-10.12, 9.88, -1.52, 8.48]}