# Application of Linear Functions in the Business World

Topics: Derivative, Polynomial, Function Pages: 21 (3010 words) Published: July 23, 2014
﻿CHAPTER ONE
Introduction
1.1 Origin of the Report

The concept of function is rightly considered as one of the most important in all of mathematics. As the point, the line, and the plane were the basic elements of Euclidean geometry, the dominant theory from the time of Ancient Greece until the Modern Age, the notions of function and derivative constitute the foundation of mathematical analysis, the theory that become central in the development of mathematics since then.

Several fields of business mathematics deal directly or indirectly with functions: mathematical analysis considers functions of one, two, or n variables, studying their properties as well as those of their derivatives; the theories of differential and integral equations aim at solving equations in which the unknowns are functions; functional analysis works with spaces made up of functions; and numerical analysis studies the processes of controlling the errors in the evaluation of all different kinds of functions. Other fields of mathematics deal with concepts that constitute generalizations or outgrowths of the notion of function; for example, algebra considers operations and relations, and mathematical logic studies recursive functions.

1.2 Objectives of the Report
Understanding the concept of functions.
To familiar with the various types of functions.
Understanding linear function and its characteristics.
Sketch the graph of linear function.
Apply linear functions in solving business problems.

1.3 Methodology
The study is application based in nature. Data used in this study are collected basically from the secondary sources. Secondary Sources:
Text and Other relevant books, Research papers
Class lecture sheets
Websites
Newspapers and Journals.

1.4 Limitation of the Study
This study has tried to figure out the key factors related to linear functions that have an effect towards the business. From the beginning to the end, the study has been conducted with the intention of making it as a complete and truthful one. But lack of adequate knowledge has an effect in   writing the report properly. However, the time period for this study was also not enough to complete the full study. 1.5 Literature Review

A linear function is an algebraic equation in which each term is a constant or the product of a constant and a variable. Linear functions appear with great regularity because so many measurable quantities are proportional to other quantities as in related linearly. Furthermore, linear functions can be helpful first approximations of computationally prohibitive nonlinear phenomena. A linear function has the following form

y = f(x) = a + bx
Where, a is the constant term or the y intercept and b is the coefficient of the independent variable Most 'real world' functions are approximations, as the world usually contains too many complications to be modeled exactly by mathematical functions. The really nice thing about linear functions is that they are easy to work with. They are easy to solve, easy to plot, and easy to understand. So when we're looking for a function to approximate the behavior of something in the real world, we usually try to use a linear function first; and only if that proves to be too simple a model do we look for other kinds of functions to use. CHAPTER TWO

Functions: Concepts & Definitions

2.1 Introduction
The function concept is one of the most fundamental concepts of modern mathematics. It did not arise suddenly. It arose more than two hundred years ago out of the famous debate on the vibrating string and underwent profound changes in the very course of that heated polemic. From that time on this concept has deepened and evolved continuously, and this twin process continues to this...

References: ‎
College Algebra with Trigonometry 7th edition by Raymond A. Barnett, Michael R. Ziegler, and Karl E. Byleen, chapter-3,graphs and functions,173
http://en.wikipedia.org/wiki/Linear_function
www.columbia.edu/itc/sipa/math/linear.html
Youschkevitch, A. P. (1976/77). The concept of function up to the middle of the 19th century. Archive for History of Exact Sciences, 16, 37-85.
Ponte, J. P. (1984). Functional reasoning and the interpretation of Cartesian graphs. Unpublished doctoral dissertation, University of Georgia, Athens.
http://classroom.synonym.com/real-life-functions-linear-equations-2608.html
Functions manual by Michael k.Chirchir and Githii Wainaina