# Thread: How do I take data from a chart and turn it into a function?

1. ## How do I take data from a chart and turn it into a function?

This is just a question I want answered so I can have fun with charts in the future.

Consider the following data:

How would make a function that hits all listed number above? Is it even possible to do so?

2. Infinitely many functions can "hit" any finite number of points.

Important questions are these:

1) Do you REALLY need it to match ALL the data? Even if there are huge outliers or other oddities?

2) What do you want it to do in between the given values?

3) What do you want it to do before and after the data start? 1989 or 2000, for example.

3. Well,

1.) I'd match it to all the data.
2.)I would want it to be smooth all the way through.
3.) This is where I'd use a limit. And caculate the next point by refering to other graphs or information to see how trends will change the graph.

4. Those are very much insufficient responses.

There are infinitely ways to be "smooth" between two points.
There are infinitely many "limits" in both directions.

What do you know about "differences"? With 10 points, you can hit all of them with a 9th degree polynomial. It's ugly, but it fits all your criteria. In this case, you are lucky enough that there is a 6th degree polynomial that is very, very close.

Really, these data do not appear to be modelled well by any elementary function. What do you know of "cubic splines"?

5. I just started with Calculus. So I know very little.

I just used that data as an example.

6. As far as turning empirical data into an equation, this is not a good place to start. Pick some data that are modelled by a line. Take the ;ast three points of your equation, for example. They are pretty close to colinear.

7. Originally Posted by TKHunny
As far as turning empirical data into an equation, this is not a good place to start. Pick some data that are modelled by a line. Take the ;ast three points of your equation, for example. They are pretty close to colinear.
He could enter the data in table 1 and 2 in his calculator and do a line of best fit of various equations. Wouldn't hit all of the points, though.

8. Well it doesn't really have to hit all points but it can come close, as in a tolerance level.