Exercise 28 Page 223

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. We can extend the line to the $y\text{-}$axis to help us find the $y\text{-}$intercept.

This line has a slope of $1$ and the $y\text{-}$intercept is $4.$ We can write the equation for this piece in slope-intercept form.