334: Which values of x do we choose? Absolutes

For the following functions, think about "How to graph like a math teacher." Math teachers want to sketch graphs quickly and efficiently and choose values of x that work "nicely" in the equation and  generate integer values of y, thus making it easier to graph.

• Which points are best found by inspection?
• Which points are best found by substitution?
• Which points are best found by symmetry?

$y = \lvert x \rvert$

$y = \lvert x \rvert - x$

$y = 2\lvert x+2 \rvert$

$y = \dfrac{1}{2}\lvert x-3 \rvert$

What are your favorite examples of this?