Exercise 34 Page 223

Let's observe the given step function.

Graphing the Function

To think about how to draw the graph, let's look at the first piece of the function. The restriction on the domain tells us that $f(x)$ equals $\text{-}2$ when $x$ is greater than or equal to $\text{-}6$ and less than $\text{-}5.$ To graph this, we draw a horizontal line at $y=\text{-}2$ extending from $x=\text{-}6$ to $x=\text{-}5.$ To indicate that $x=\text{-}6$ is contained in the solution set, we place a closed circle at that point. $x=\text{-}5$ is not contained in the solution set of this piece, which we indicate with an open circle.

Following a similar process, we can graph the other pieces of the function.

Domain and Range

Now that we have graphed the function, we can describe its domain and range.

Domain

The domain of a function is the set of $x\text{-}$values for which the function is defined. From the graph (and the function rule), we can see that $x$ can equal any value from $\text{-}6$ to $0,$ not including $0.$

Range

The range of a function is the set of $y\text{-}$values for which the function is defined. From the graph (and the function rule), we can see that $y$ can only equal $\text{-}2,\text{-}1,0,$ and $1.$