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Relations and Functions.tex
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\documentclass[10pt]{article} \usepackage{amssymb,amsmath} \usepackage[hmargin=1cm,vmargin=1cm]{geometry} \begin{document} {\large Relations and Functions} \begin{align*} \text{Relations:}\quad&\text{A mapping from a set of real numbers to a set of real numbers.}\\ \text{i.e. }&D\to R.\quad\text{(At this stage, }D\subseteq\mathbb{R}\text{ and }R\subseteq\mathbb{R}\text{).}\\ &\text{$D$ is called the \it Domain\rm, and $R$ is called the \it Range\rm.}\\ \\ &\text{When the relation is represented as $f(x,y)=0$, then}\\ &\quad x\in D\text{, and is called the independent variable. Its values are \it input values\rm.}\\ &\quad y\in R\text{, and is called the dependent variable. Its values are \it output values\rm.}\\ \\ &\text{A function is a relation in which there is only one output for each input value in $D$.}\\ &\quad\text{A function is represented as $y=f(x)$.}\\ \\ &\text{Even function:}\qquad f(x)=f(-x)\quad\text{(Symmetrical around y-axis.)}\\ &\text{Odd function:}\qquad f(x)=-f(-x)\quad\text{(Symmetrical around the origin.)}\\ \\ \text{Locus:}\quad&\text{A set of points that satisfy a condition.}\\ &\text{All points on the locus satisfy the condition,}\\ \text{\it and}\:\:&\text{all points satisfying the condition are on the locus.}\\ \end{align*} \end{document}