Graphs, equation and functions.

[Nemika]

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?

 

[paisiello2]

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.

 

[Nemika]

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

 

[paisiello2]

I think it's irrelevant. You can always come up with an equation that will go through all your data points.

 

[Nemika]

OK, and if it is an equation can it be a function

 

[Mark44]

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.

 

[Nemika]

How can we determine that an equation is a function or not

 

[HallsofIvy]

Do you know the definition of "function"?