Algebra-polynomial and rational functions

Reference no: EM13119942

One of the advantages of rational functions is that even rational functions with low-order polynomials can provide excellent fits to complex experimental data. Linear-to-linear rational functions have been used to describe earthquake plates. As another example,
a linear-quadratic fit has been used to describe lung function after patients have been treated with x-rays; cubic/quadratic equations are used to model the stiffness of various materials.

To explore the versatility of rational functions, choose a second-order/third-order (e.g., x2/x3) and a third-order/second-order (e.g., x3/x2) rational function. Provide a graph for the second-order rational function (e.g., x2), choosing x values in the range from -10 through +10.

Then, provide at least three variations of the function plotted on the same graph. Include separate changes to a coefficient in the numerator, to a coefficient in the denominator, and to a constant. The changes should be increases or decreases of a factor of 2 in each case. Repeat the procedure making a second graph for the third-order rational function (e.g., x3). For each of the two graphs, describe how changes in coefficients and constants change the behavior of the function.

Please give explanation and references.

Reference no: EM13119942

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