2.1 Introduction

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

$y = x + 3$ $y = x + 3$

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

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

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

$y = x^{2} - 10$ $y = x^{2} - 10$

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

As another example, take the following function:

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

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

A rational functionrational function: A function that can be written as the quotient of two polynomial functions where the function in the denominator is non-zero. 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:

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

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

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

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

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