Curve Sketching, How to get the Function?

[Dragonetti]

Hi,
I have a question regarding curve sketching.

I am fairly competent in sketching curves from a function, i.e. x²+2x, etc.

But how would I go about getting the function of a curve?

Lets say I sketched a freehand curve ,
Would I have to draw a set of axes onto the curve and then take coordinates at certain points, Or is there an easier way, using differentiation maybe?

Thanks
Dominic

 

[HallsofIvy]

That is, in fact, a crucial question- any time a scientist, chemist, engineer, etc. does experiments, he/she gets "data points" which could be used to sketch a curve in the appropriate coordinate system.

However, given any finite number of data points, there exist an infinite number of functions that will give those points. Typically what you must do is assume some appropriate kind of function (polynomial, exponential, trig, etc.) with undetermined coefficients. The put the x and y values of your graph into that formula to get equations to solve for the coefficients.

Yes, you certainy would have to set up axes in order to have numerical values to work with. A "curve" alone does not have numerical values and does not define any function, which is all about numerical values.