Graphing Parametric Equations with Non-Linear Constraints

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Discussion Overview

The discussion revolves around graphing parametric equations defined by x = t and y = 2t, with the additional condition that y ≠ f(x). Participants explore the implications of this condition and how it affects the graphing of the equations.

Discussion Character

  • Exploratory, Debate/contested, Technical explanation

Main Points Raised

  • One participant suggests plotting a point for every t or calculating y = f(x).
  • Another participant argues that the condition y ≠ f(x) is nonsensical, as the definitions imply y = 2x, which can be easily graphed.
  • A similar point is reiterated by another participant, emphasizing that y ≠ f(x) does not hold in this case.
  • Some participants propose that the lack of a function for y in terms of x may be due to cases where multiple y values correspond to a single x value, but they acknowledge that a function can be defined here as f(x) = 2x.
  • There is a suggestion that the original poster may have meant y ≠ t instead of y ≠ f(x).

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of the condition y ≠ f(x), with some asserting it is nonsensical while others attempt to clarify its implications. The discussion remains unresolved as to the intent behind the condition.

Contextual Notes

The discussion highlights potential confusion regarding the definitions of the variables and the implications of the condition y ≠ f(x), which may depend on the context of the problem.

mymachine
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If x = t, y = 2t, and y ≠ f(x), how to graph these equations?
 
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Plot a point for every t.
Alternatively, calculate y=f(x).
 
Your condition y ≠ f(x) doesn't make sense. The definitions you give for x and y imply y = 2x, which is easily graphed.
 
mathman said:
Your condition y ≠ f(x) doesn't make sense. The definitions you give for x and y imply y = 2x, which is easily graphed.

In this case, y is ≠ f(x).
 
mymachine said:
In this case, y is ≠ f(x).

Possibly what you mean to say is that no function has been given for y in terms of x.

In some cases it is true that no function exists for y in terms of x. This would be because there are some values of x that pair up with more than one value for y. However, in the case at hand, it is trivial to find an f() such that y = f(x).
 
mymachine said:
In this case, y is ≠ f(x).

f(x) = 2x. What does your assertion mean?
 
Maybe he meant for y ≠ t?
 

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