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Polynomial and Rational Functions

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* Create a set of data that can be modeled as a polynomial function.
* Please provide a reference to the data. Plot the data using Microsoft Excel including the equation for the fit.
* Discuss how closely the data seem to match to the best fit line

What type of information can you use for this that you could find in an everyday situation? PLEASE HELP!

Then I need to do the same for data that can be modeled using a rational function.

I'm not clear what type of data I can use for this one. I need to provide two graphs, their data and the equation for them.

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Solution Summary

The solution defines "function", "polynomial", and "rational function". Then it gives examples of data that can be modeled using a polynomial or a rational function and shows how to make a scatterplot and find the best-fit function in Excel.

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First things first ... a function is an equation relating two variables (usually called x and y) so that when you pick a value for x, there's only one possible value for y to make the equation true.

A polynomial function is a function where all the terms with x in them have coefficients that are real numbers and exponents that are whole numbers. (Some more definitions: a coefficient is the number that the variable is multiplied by, and an exponent is the power that the variable is raised to. Whole numbers are 0, 1, 2, 3, ...) Some examples of polynomials are:
y = x
y = -3x + 5
y = 3
y = 3x2 - 8x + 1
y = 8x95 + 4x3 - 3x2 + 9
The following are not polynomials:
y = x-2
y = √x + 5
y = 3x

A rational function is a function that is created by dividing one polynomial by another (the only exception is that you can't divide by 0).

POLYNOMIAL FUNCTION

So first, we have to find data that can be modeled using a polynomial function. We need to find data with x and y values that we think will look like a polynomial when we graph x and y. Simple examples of polynomials are lines (when the equation looks like y = a or y = ax + b) and parabolas (where the equation looks like y = ax2 + bx + c).

I found data at this website: http://www.census.gov/compendia/statab/vital_statistics/ (108 - Age-Adjusted Death Rates by Major Causes: 1960 to 2004). ...

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