Exercise 9 Page 219

To write the piecewise function for the given graph, we need to find the equation of the line representing each piece and then restrict the domain accordingly.

The First Piece

Let's begin by finding the slope and $y\text{-}$intercept of the first piece of the function.

This line has a slope of $\text{-}1$ and the $y\text{-}$intercept is $\text{-}1.$ We can write the equation for this piece in slope-intercept form.

The Second Piece

Now let's take a look at the second piece.

This line has a slope of $1$ and the $y\text{-}$intercept is $2.$ We can write the equation for this piece in slope-intercept form.

Combining the Pieces

We can add the equations of these lines to the piecewise function notation. Finally, we need to determine the domain for each equation. The jump occurs at $x=0,$ so this will be where the domains are divided. We cannot have an overlap in our domains so we need to take notice of where the closed and open circles are located. The closed circle at the end of the first piece tells us that its domain includes $0.$ The open circle at the beginning of the second piece tells us that its domain does not include $0.$