Graphing Absolute Value Functions

To graph the given absolute value function, we will start by making a table of values. To do so, we will assign some random values to the $x\text{-}$variable and calculate the corresponding values of the $y\text{-}$variable.

Let's now plot and connect the obtained points on a coordinate plane. Recall that the graph of an absolute value function has a V shape.

We see above that the $x\text{-}$variable can take any number. We also see that the $y\text{-}$variable takes values greater than or equal to $3.$ With this in mind, we can write the domain and range of the function. $$\begin{array}{rl}\text{Domain:}& \text{all real numbers}\\ \text{Range:}& y\ge 3\end{array}$$