Polynomials and Rational Functions

Polynomials and rational functions:

Researchers will frequently collect lots of discrete samples of data, relating two or more variables, devoid of knowing the mathematical relationship among them. Curve fitting is mainly used to form trend lines intended to fill up in the points among and beyond the collected data points.

Polynomial functions are simple to use for the modeling however ill-suited to modeling asymptotes and a few functional forms, and they can become much inaccurate exterior to the bounds of collected data.

Rational functions can get on a much bigger range of shapes and are much accurate both within and outside the limits of the collected data than polynomial functions. Though, rational functions are much hard to use and can comprise undesirable asymptotes.

Basic definition:

Constant function: It is a polynomial function in one variable of the degree 0.

Polynomial form: f(x) = a0
Standard form: f(x) = c

Linear function: It is a polynomial function in one variable of the degree 1.

Polynomial form: f(x) = a1x + a0
Standard form: f(x) = ax + b

Quadratic function: It is a polynomial function in one variable of the degree 2.

Polynomial form: f(x)= a2x2 + a1x + a0
Standard form 1: f(x) = ax2 + bx + c
Standard form 2: f(x) = a (x-h)2 + k

Cubic function: It is a polynomial function in one variable of the degree 3.

Polynomial form: f(x)= a3x3 + a2x2 + a1x + a0

Key topics included in this chapter are as follows:

a) Quadratic Functions
b) Polynomial Functions of Higher Degree
c) Real Zeros of Polynomial Functions
d) The Fundamental Theorem of Algebra
e) Rational Functions and Asymptotes
f) Graphs of Rational Functions

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