Hi Guys
This is NOT homework! My homework was to do the opposite.
I’m wondering if it’s possible to derive a function if you are given a plot drawn on a graph?
This is totally arbitrary. A function didn’t create it. I made it up.

It’s to accelerate quickly from zero toward 32 or 33, and slow down toward the end.
You could think of the list of integers as a lookup table, so that x0 ouputs y0,
x32 outputs y32, but incrementing in-between is not a linear output.
I wouldn’t expect the output of a similar function to be integers of course, for a curve,
but maybe the floats would round to approximate the integers.
Cheers, Art.

 

I’m wondering if it’s possible to derive a function if you are given a plot drawn on a graph?

Sure, it’s called curve fitting and it doesn’t matter whether you do y vs x or vice versa.

Curve fitting can be a bit of an art and it helps to understand the system. For instance the rate of a chemical reaction typically obeys the Arrhenius equation, and so transforming the data to fit that will give you a straight line. Same deal with exponential growth of microbes or exponential decay of voltage on a capacitor in an RC circuit. Plotted properly these can all be straight lines which are far easier to fit.

 

Simple! I don’t know why the solution didn’t just dawn on me intuitively:
y = 37.00346+(-0.3649253-37.00346)/(1+(x/9.347271)^1.414382)

One of those parenthesis of constants can be eliminated,
but somehow, I’m not sure this is a saving on my original 33 byte lookup table

Thanks the the reply in any case, I really do appreciate it

 

Curve fitting can take many forms, least squares, power.....

https://en.wikipedia.org/wiki/Curve_fitting


Regards, Dana.

 

Hi Guys
This is NOT homework! My homework was to do the opposite.
I’m wondering if it’s possible to derive a function if you are given a plot drawn on a graph?
This is totally arbitrary. A function didn’t create it. I made it up.

It’s to accelerate quickly from zero toward 32 or 33, and slow down toward the end.
You could think of the list of integers as a lookup table, so that x0 ouputs y0,
x32 outputs y32, but incrementing in-between is not a linear output.
I wouldn’t expect the output of a similar function to be integers of course, for a curve,
but maybe the floats would round to approximate the integers.
Cheers, Art.

You can do it provided the graph actually is a function. In order to be a function, it must be single-valued. For y(x), this means that for any given value of x, there is exactly one value of y.

If that requirement is satisfied, then you can come up with a mathematical function that approximates the actual graph as close as you want it to, but the closer you want it, the more complicated the function gets.

 

In order to be a function, it must be single-valued. For y(x), this means that for any given value of x, there is exactly one value of y.

This statement is demonstrably false – the function for a circle has 2 separate values for y for any given value of x.

 

This statement is demonstrably false – the function for a circle has 2 separate values for y for any given value of x.

And it is therefore not a function. Spend some time looking at what the definition of a mathematical function IS, as opposed to what you would like it to be.

It might help to look at the difference between a relation and a function.

 

And it is therefore not a function. Spend some time looking at what the definition of a mathematical function IS, as opposed to what you would like it to be.

It might help to look at the difference between a relation and a function.

I bow to your superior knowledge – but the ‘circle equation’ shows that it is not a requirement for the solution to be a function.

 

I bow to your superior knowledge – but the ‘circle equation’ shows that it is not a requirement for the solution to be a function.

A circle is a function when described by angle and range.