Exercise 27 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 intercept.

Notice that the graph is a part of a horizontal line. We know that a horizontal line has a slope of $0.$ The $y\text{-}$intercept of our line is $1.$ We can write the equation for this piece in slope-intercept form.