Creating a Function from Points: How to Get Started

So you can solve for those coefficients, and thus find the polynomial.In summary, if you have exact values for 5 points, you can use any function to create a graph that passes through them. However, if you want to use a polynomial, you will need 5 distinct points to find a unique polynomial of degree 4 that passes through them.
  • #1
Juan Pablo
40
0
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!
 
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  • #2
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)?
 
  • #3
The points are exact, I can use any function
 
  • #4
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
[tex]y= a_nx^n+ a_{n-1}x^{n-2}+ \cdot\cdot\cdot+ a_2x^2+ a_1x+ a_0[/tex]
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 an, ..., a1, a0.
 

1. How do I determine the function from a set of points?

To determine the function from a set of points, you will need to first plot the points on a graph. Then, look for patterns or trends in the data. If the points form a straight line, you can use the slope-intercept form (y = mx + b) to determine the function. If the points do not form a straight line, you can use other methods such as the point-slope form or the general form of a linear equation (Ax + By = C) to find the function.

2. What if there are too many points to plot on a graph?

If there are too many points to plot on a graph, you can use a spreadsheet or a graphing calculator to input the data and create a scatter plot. From there, you can use the same methods mentioned above to determine the function.

3. Can I use any points to create a function?

Yes, you can use any set of points to create a function. However, it is important to note that the more points you have, the more accurate your function will be. It is recommended to have at least three points to create a linear function and more points for nonlinear functions.

4. Are there any specific rules or steps to follow when creating a function from points?

There are no specific rules or steps to follow when creating a function from points. However, it is important to plot the points accurately, look for patterns or trends in the data, and use the appropriate form of the linear equation to determine the function.

5. Can I use a function to predict values for points that are not given?

Yes, you can use a function to predict values for points that are not given. This is one of the main purposes of creating a function from points. By using the function, you can find the corresponding y-value for any x-value on the graph.

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