[Solved] polynomial and rational functions

A function is a representation of the dependent variable function in terms of the dependent variable(s). There are different kinds of functions to model different situations we encounter in real world. Polynomial and rational functions are two such functions. In subsequent sections we will briefly look at these functions.

Polynomial Function

Polynomial functions are represented as , where y is the dependent function, x is the independent function, n is a whole and ai are the coefficients. An example of polynomial function from the real world is the distance of an object from a point, the object is moving in a straight line with a constant acceleration is given by the following function:

Where s is the distance at time t, so is the distance at t = 0, u is initial velocity i.e. velocity at t = 0 and t is the time.

The data was plotted using MS Excel. The plot is present below in figure 1. A second order polynomial was fitted. The best fit equation is  and the value of R2 is 0.9999. A value of R2 close to 1.0 means very good fit of the data into the model equation. Thus it can be said that the data fits excellently into the second order polynomial. The coefficients give parameters like initial velocity u = 4.8507 m/s and acceleration a = 5.0382 m/s2.

Rational Function

Rational functions are defined as , where P(x) and Q(x) are two polynomials. Suppose, we define a parameter “Lead Ratio (LR)” as ratio of the distance traveled by two cars. One can calculate lead for two cars as .

Thus we find that polynomial and rational functions are very useful for modeling many real life situations.

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