If one were trying to streamline the Algebra 2 curriculum, is there a good argument for retaining the rules of thumb by which we were all taught to graph rational functions by hand (finding asymptotes, holes, intercepts, all of that)? Or could we hand that over to graphing calculators and e.g. teach students a bit more probability theory?
The inevitable clarification:
1) Functions and their properties are central to math education.
2) I'm not proposing that we replace math with button-pushing.
3) In fact, memorizing a set of arbitrary procedures (if degree of the numerator is less than than the degree of the nominator, plug in this. If the degree of the numerator and denominator are the same, plug in that.) seems like just old-school button-pushing.
4) I wonder if rational functions are particularly low-hanging fruit to trim.
@ct_bergstrom Think that if you trim rational functions, your only remaining singularities will be in things like tan and sin⁻¹
