Math Arguments

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

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Item 186

Which values of x do we choose? Rational functions

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?


\(y = \dfrac{4}{(x+2)(x+11)}\)

\(y = \dfrac{1}{x^2+1}\)

\(y = \dfrac{1}{x^-1}\)

\( y = \dfrac{x+2}{x^2-4}\)

\( y=\dfrac{x^2-1}{x^2+1}\)

What are your favorite examples of this?


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Smart Substitution
T.R.Milne
ALG2

Source: T.R.Milne
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