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.
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Evaluate piecewise functions by Khan Academy
Next, students will 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 these challenges:
Express abs in terms of max. The answer is
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
Mentally determine what fraction is shaded.

Answer: \((3/16)\pi\)
Conclude by leading this investigation:
The Broken Sword (addition, division, mini-mathematical universe)
by MathPickle