Students will learn how to evaluate unary piecewise functions, including the absolute value function and piecewise linear functions. They'll evaluate using either the function's definition or its graph. The second problem in this video is a word problem requiring students to evaluate a piecewise function from its graph. Students will also learn how to model piecewise functions from word problems (video). After that, students will learn the definitions of \(\text{min}(x,y)\) and \(\text{max}(x, y),\) and how to evaluate these functions for various inputs. For example, \(\text{max}(3, 2) = \mathop{?}\) Next, give your students the following challenge: Express abs in terms of max. The answer is
$$\lvert x \rvert = \max(x, -x)$$Finally, give your students this challenge: Express \(\max\) in terms of \(\text{abs}.\) Then use your answer to express \(\max(x, 0)\) and \(\min(x, 0)\) in terms of \(\text{abs}.\) The answer is
$$\begin{align} & \max(x, y) = \dfrac{x + y + \lvert x - y \rvert}{2} \\[1em] & \max(x, 0) = \dfrac{x + \lvert x \rvert}{2} \\[1em] & \min(x, 0) = \dfrac{x - \lvert x \rvert}{2} \end{align}$$