Graphs, equation and functions.

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Discussion Overview

The discussion revolves around the relationship between graphs, equations, and functions, exploring whether a curve or other shapes represented on a graph can be expressed as equations and whether those equations can be classified as functions. The scope includes conceptual clarifications and technical reasoning regarding mathematical definitions and relationships.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that if a relation is represented on a graph as a curve, it can be expressed in the form of an equation.
  • Another participant counters that the shape being a curve is irrelevant, asserting that an equation can always be fitted to a set of points, though its accuracy in describing the relationship is uncertain.
  • A later post reiterates the idea of curves or hyperbolas being representable as equations.
  • Some participants argue that it is possible to create an equation that passes through all data points, regardless of the shape of the graph.
  • There is a question raised about whether an equation can also be classified as a function.
  • One participant states that not all equations represent functions, providing the example of the equation of a circle, which does not qualify as a function.
  • A question is posed regarding the criteria for determining if an equation is a function.
  • Another participant asks if the definition of "function" is understood, implying a need for clarity on the term.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of the graph's shape to its representation as an equation, and there is no consensus on whether all equations can be classified as functions. The discussion remains unresolved regarding the criteria for determining functions.

Contextual Notes

There are unresolved assumptions regarding the definitions of functions and the criteria for fitting equations to data points. The discussion does not clarify the mathematical steps involved in determining whether an equation represents a function.

Nemika
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Is it correct to say that if a relation between a few numbers is represented on a graph and it comes out to be a curve than it can be written in the form of an equation?
 
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First of all, I don't think it needs to be a curve, that is irrelevant.

Secondly, you can always fit an equation to a set number of points. Now whether this equation describes the relationship accurately or not is another question.
 
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I mean to say that if it happens to be a curve or hyperbola than can it be represented in the form of an equation
 
I think it's irrelevant. You can always come up with an equation that will go through all your data points.
 
OK, and if it is an equation can it be a function
 
Nemika said:
OK, and if it is an equation can it be a function
No. Many equations do not represent functions. For example, ##x^2 + y^2 = 1## is the equation of a circle. This equation does not represent a function.
 
How can we determine that an equation is a function or not
 
Do you know the definition of "function"?
 

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