Exercise 10 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. To help us write the equation of the line for this piece, we can extend the line to the $y\text{-}$axis. This will help us to know the $y\text{-}$intercept.

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