Creating a Function from Points: How to Get Started

[Juan Pablo]

Just out of curiosity, is it possible to get a function from, say 5 points? If so how?
I don't want a full explanation just someone to point me to the right direction.

Thanks!

 

[Borek]

You can put a straight line through every 5 points, it just have to be thick enough.

Question is so vague that it is impossible to answer. Are points known exactly, or are their values only approximate? Are you allowed to use any function, or only functions from some set (like polynomials)?

 

[Juan Pablo]

The points are exact, I can use any function

 

[HallsofIvy]

Given any finite number of points, there exist an infinite number of functions whose graph passes thorough them. (As long as all points have different x values, of course.) Given n+1 points, there exist a unique polynomial of degree n whose graph passes through them. You could for example write the polynomial as
$$y= a_nx^n+ a_{n-1}x^{n-2}+ \cdot\cdot\cdot+ a_2x^2+ a_1x+ a_0$$
Replacing x and y with the n+ 1 x and y values from the n+ 1 points gives you n+1 equations for the n+1 coefficients a_n, ..., a₁, a₀.