Discussion Overview
The discussion revolves around the capability of the TI-89 calculator to graph equations that are not explicitly defined as functions of the form f(x). Participants explore the potential for graphing implicit functions and the methods available to achieve this.
Discussion Character
- Technical explanation
- Exploratory
- Debate/contested
Main Points Raised
- One participant inquires about graphing equations like 2x + 3y = 7 and 3y^2 + 2x^2 - 3x + 6 = 0 on the TI-89.
- Another participant suggests that if y = f(x), one should solve for y, indicating that the TI-89 can handle such transformations.
- A third participant expresses confidence that only explicit functions can be graphed on the TI-89, reiterating the need to solve for y.
- One participant mentions that implicit functions can sometimes be graphed using parametric equations, providing the example of a circle defined by x^2 + y^2 = 1.
- Another participant notes that the TI-89 is programmable and suggests looking for packages or writing custom programs to enhance its graphing capabilities.
- A later reply indicates that it is possible to write a program to graph implicit equations directly without solving for a variable first.
Areas of Agreement / Disagreement
Participants express differing views on the capabilities of the TI-89 regarding implicit functions. While some suggest that explicit forms are necessary, others propose alternative methods such as parametric graphing or programming solutions. The discussion remains unresolved regarding the best approach to graphing non-explicit functions.
Contextual Notes
Participants mention various methods for graphing, including solving for variables and using parametric equations, but do not reach a consensus on the limitations or capabilities of the TI-89 in handling implicit functions.