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?
@ct_bergstrom Maybe is useful to be able to logically deduce asymptotes, intercepts, singularities, etc., for reasons more important than graphing them? Also is easy to graph things with Matlab or Jupyter and not notice the singularities
@ct_bergstrom Think this is actually more important than solving equations. Intuition for how things act at x → ∞, x → -∞, x = 0, y = 0, denominator → 0 is street fighting mathematics.
@radehi @ct_bergstrom this is my thinking, too. I teach graphing rational expressions in a intro calc course in high school rather than in algebra II. It’s a warm up for thinking about the infinite (asymptotic behavior) and infinitesimal (removable discontinuities). And it’s excellent review and consolidation of basic algebra and even fractions.