inverse function command

[jonmoore]

Apologies for dredging up this old discussion, but it's something I was teaching my youngest about last night so I thought it apt.

What the OP was asking for, is an equivalent of the DrInv command on the TI-86 (it's called DrawInv on the TI-84/83 family of calculators - ref: https://www.dummies.com/article/technolo...us-160952/)



In the classic "Investigations in Mathematics (for the HP 48G/GX)" a solution for the lack of this function on the 48G/GX was a clever program devised by Bill Wickes that drew a Parametric Plot over the original Function Plot.



People often ask why TI hammered HP in the education sector and the lack of this vital visualisation routine in HP calculators sums things up perfectly for me. Sure I understand Joe's pedagogic argument ref the by hand algebraic solution, but I've always found that using visualization to teach underlying algebraic rules is often the best way to cement algebraic insight.

The same authors behind Investigations in Mathematics (Donld's Latorre and Kreider) were also responsible for the massively influentic 'Calculus Conceps - An informal Approach' series of books. The content for this book was originally devised at Dartmore College (of BASIC fame) when the HP-28C was released in the late eighties. The book series started with the HP-48G/GX front and centre, alongside TI's 83/84/85 & 86 (it was first released in the early/mid nineties), but by the early naughties, the book series focus had moved to the TI's 84 & 89 alone (and Microsoft Excel).

There's no argument to the fact that HP's 48/49/50 series of calculators are more powerful and flexible than anything TI have ever released. But TI pumped lots of resources into curriculum outreach. Their calculators have less functions than HP calculators because it's what teachers and the majority of students wanted. HP may have released cheaper models for the education market with less features but the included functions were never as finely tuned to curriculum needs as those provided with the TI's.

Getting back to DrInv/DrawInv. The thing that amazes me, is that HP got feedback from LaTorre & Krieder back in the early nineties that this was an important function, and Bill Wickes devised a program to remidy that need. But that's as far as it went. The HP design team didn't use that feedback to provide a 'draw inverse function' capability into later calculators. In the preliminary edition of the graphing calculator instruction guide for 'Calculus Concepts - an Informal Approach', the HP 48G/GX required 27 bespoke routines to be entered into the calculator (some very lengthy), so it could be used to follow the text (the TI-83 and 85 only required 5 bespoke programs as everything else was already part of their native function-sets).

There were many other great routines for the 48 included in the Calculus Concepts graphing calculator guides as well as the draw inverse function routine. But none of these routines were included in future HP calculators. All of the bespoke programs for the TI 83/85 became native functions in future TI models (things like logistic regression and more flexible curve fitting). I'm not sure if it was oversight or arrogance that meant the HP design team didn't see the need (and benefit) of integrating any of the bespoke routines in future graphical models but it was most definitely a major oversight. TI cemented their reputation for providing curriculum focused solutions and HP increased their reputation for providing powerful solutions where complexity was often a barrier to usability - and this is the last thing you need in a classroom scenario, as you spend more time teaching the calculator feature-set, than the core mathematical concepts of the lesson content!