Finding the Equation of a Function.

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Discussion Overview

The discussion revolves around finding an equation for a function based on a given set of points: (0, 2), (1, 4), (2, 10), and (3, 28). Participants explore different approaches to represent this function, including polynomial forms and recurrence relations.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant suggests trying a cubic polynomial of the form $ax^3 + bx^2 + cx + d$ and substituting the given values to solve for the coefficients.
  • Another participant introduces a recurrence relation, stating that $a_{n+1} = a_n + 2 \cdot 3^{n-1}$ with an initial condition of $a_0 = 2$, indicating a different method to represent the function.
  • A third participant notes that subtracting 1 from the function values might reveal a familiar sequence, hinting at a potential transformation or simplification.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single method for representing the function, as multiple approaches are proposed and explored without resolution.

Contextual Notes

The discussion does not clarify the assumptions behind the proposed polynomial form or the recurrence relation, nor does it address any potential limitations in the methods suggested.

vivalajuicy
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The following points are part of a table of values for a function.
(0, 2), (1, 4), (2, 10), (3, 28)
Represent this function as:
a) equation
 
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Try a cubic of the form $ax^3+bx^2+cx+d$ substitute your values to solve for $a,b,c,d$ , what do you get?
 
Hello, vivalajuicy!

The following points are part of a table of values for a function:
. . (0,2), (1,4), (2,10), (3,28)
Represent this function as: (a) equation
I don't have the equation yet, but I have a recurrence.

. . a_{n+1} \;=\;a_n + 2\!\cdot\!3^{n-1},\;\;\;a_0 = 2
 
vivalajuicy said:
The following points are part of a table of values for a function.
(0, 2), (1, 4), (2, 10), (3, 28)
Represent this function as:
a) equation
The values of the function are 2, 4, 10, 28. If you subtract 1 from each of those, it may give you a sequence that looks familiar.
 

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