2.1 Introduction

In this chapter, we will explore polynomial and rational functions. A polynomial function is a function of a single independent variable. The independent variable ($x$) can appear multiple times, raised to any non-negative integer power. The following are examples of polynomial functions:

$y=x+3$

$y=3x^4-2x^2-100$

$y=-100x^{1}20-30x^3+x-120$

When we talk about $n$th degree polynomial, $n$ is the highest power to which the independent variable is raised. For example,

$y=x^2-10$

is a second-degree polynomial since 2 is the highest power that the independent variable $x$ is raised to.

As another example, take the following function:

$y=x^5-3x^7+2x^2-x+30$

This is a seventh-degree polynomial since 7 is the highest power that the independent variable is raised to.

A rational function is a function that is the quotient of two polynomials with a denominator that has a degree of at least 1. Here are some examples:

$y=\frac{x^2-3}{x+2}$

$y=\frac{-3x^5+2x^3-5x+1}{x^2-3x-5}$

$y=\frac{-x+100}{x^3+x-4}$

In this chapter, we will learn the basics of polynomial and rational functions and understand how they are applicable in the business world.