# How do you graph f(x)=2^(x-1)-3 and state the domain and range?

Feb 3, 2018

Domain: $\left(- \infty , \infty\right)$

Range: $f \left(x\right) > \left(- 3\right)$

#### Explanation:

Given:

$\textcolor{b l u e}{y = f \left(x\right) = {2}^{x - 1} - 3}$

Refer to the graph below to understand the behavior of the given exponential function:

graph{2^(x-1)-3 [-10, 10, -5, 5]}

Let us look at the table given below:

We observe that the domain will be all real values.

For every value of $x$ there is a corresponding $y$ value.

Hence

Domain: $\left(- \infty , \infty\right)$

Below you find a representation of both the parent function color(green)(y=2^x and y = 2^(x-1)-3

We find a horizontal asymptote at $y = - 3$

Hence Range: $f \left(x\right) > \left(- 3\right)$