# How can I get a function relation with these two sets?

• zeion
In summary, the conversation discusses finding a function relation for sets of points, specifically (1, 1) (2, 3) (3, 9) (4, 10) and (1, 1) (2, 5) (3, 12) (4, 22). The suggestions include using algebra, fitting a polynomial, and using a website such as oeis.org to find patterns and corresponding functions. The specific function mentioned is the Pentagonal numbers, n*(3*n-1)/2.
zeion

## Homework Statement

I have these two sets:

Pairwise, (1, 1) (2, 4) (3, 9) (4, 16). Clearly this is just squared.

How can I get a function relation with like:
(1, 1) (2, 3) (3, 9) (4, 10)

or like

(1, 1) (2, 5) (3, 12) (4, 22)

## The Attempt at a Solution

I know it is exponential...
Can I do something with log?

Any number of ways. You could just fit a polynomial to them if you only have four points.

Do I need a program to do it or can I do it by algebra..?

Sure you can do it by algebra. Write y=x^4+a*x^3+b*x^2+c*x+d. Put in your four x and y values. That gives you a system of four linear equation in a,b,c,d. Solve them. It's certainly easier using a program, but you can do it by hand.

Thanks!

## 1. How do I determine if there is a function relation between two sets?

To determine if there is a function relation between two sets, you can use the vertical line test. If a vertical line drawn on a graph of the sets intersects the graph at only one point, then there is a function relation between the two sets.

## 2. What is the process for finding a function relation between two sets?

The process for finding a function relation between two sets involves examining the elements in each set and determining if there is a one-to-one correspondence between them. This means that each element in one set is paired with exactly one element in the other set.

## 3. Can a function relation exist between two sets if they have the same elements?

Yes, a function relation can exist between two sets even if they have the same elements. The key factor is the way in which the elements in one set are related to the elements in the other set.

## 4. How can I write a function relation between two sets as an equation?

To write a function relation between two sets as an equation, you can use the standard form of a function, which is y = f(x). The x values represent the elements in the first set and the y values represent the elements in the second set. You can then plug in the values from each set to create the equation.

## 5. What is the difference between a function relation and a one-to-one function?

A function relation refers to the relationship between two sets, where each element in one set is paired with an element in the other set. A one-to-one function, on the other hand, is a specific type of function where each input has only one output and each output has only one input. All one-to-one functions are function relations, but not all function relations are one-to-one functions.

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