Discussion Overview
The discussion revolves around how to graph two functions, X = -y and X = 2y - y², on a TI-89 Titanium calculator, where the standard graphing mode is set for y as a function of x. Participants explore various methods to adapt the calculator's functionality to accommodate the functions expressed in terms of y.
Discussion Character
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant suggests replacing y with x and vice versa in the calculator while keeping track of the notation change.
- Another proposes a rotation transformation of the coordinates, suggesting (x, y) transforms to (y, -x) to facilitate graphing.
- A different approach involves using PARAMETRIC mode, with y set as a function of a parameter t, such as y = t and x = 2t - t².
- One participant mentions using the SOLVE function to find y in terms of x, indicating that roots must be manually entered for certain functions.
- Another participant expresses difficulty in replicating the graph despite trying the suggested methods, indicating a need for further clarification.
Areas of Agreement / Disagreement
Participants present multiple competing methods for graphing the functions, and there is no consensus on a single best approach. Some methods are suggested as potential solutions, but participants express varying levels of success with these methods.
Contextual Notes
Some participants mention specific settings, such as tstep = 0.05 in PARAMETRIC mode, but there are unresolved issues regarding the exact implementation of these methods on the calculator.