Math Arguments

Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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Item 184

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 in the graph
- are best found by inspection?
- are best found by substitution?
- 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?


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Smart Substitution
T.R.Milne
ALG1

Source: T.R.Milne
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