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\QTR{small}{Matematick\U{e1} anal\U{fd}za I online - Funkcie - Graf funkcie\dotfill \thepage }} %} \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex} \begin{document} \author{A. U. Thor} \title{Lab Report} \date{The Date } \maketitle \begin{abstract} A Laboratory report created with Scientific Notebook \end{abstract} \section{Funkcie} \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|} \hline \textbf{% %TCIMACRO{\hyperref{Obsah}{}{}{maindex.tex}}% %BeginExpansion \msihyperref{Obsah}{}{}{maindex.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Obsah kapitoly}{}{}{M2.tex}}% %BeginExpansion \msihyperref{Obsah kapitoly}{}{}{M2.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Predch\'{a}dzaj\'{u}ca str\'{a}nka}{}{}{M22.tex}}% %BeginExpansion \msihyperref{Predch\'{a}dzaj\'{u}ca str\'{a}nka}{}{}{M22.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Nasleduj\'{u}ca str\'{a}nka}{}{}{M24.tex}}% %BeginExpansion \msihyperref{Nasleduj\'{u}ca str\'{a}nka}{}{}{M24.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Ot\'{a}zky}{}{}{O2.tex}}% %BeginExpansion \msihyperref{Ot\'{a}zky}{}{}{O2.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Cvi\v{c}enia}{}{}{C2.tex}}% %BeginExpansion \msihyperref{Cvi\v{c}enia}{}{}{C2.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Index}{}{}{G1.tex}}% %BeginExpansion \msihyperref{Index}{}{}{G1.tex}% %EndExpansion } \\ \hline \end{tabular} \end{center} \subsection{Graf funkcie} Niekedy je vhodnej\v{s}ie a in\v{s}trukt\'{\i}vnej\v{s}ie miesto \ popisu funkcie pomocou formuly, alebo tabu\v{l}ky na\v{c}rtn\'{u}\v{t} obr\'{a}zok funkcie. To je aj \'{u}lohou matematickej anal\'{y}zy, aby sme vedeli na\v{c}% rtn\'{u}\v{t} obr\'{a}zok danej funkcie. Obrazov\'{a} reprezent\'{a}cia funkcie sa naz\'{y}va graf funkcie \begin{definition} \label{1}Nech $f:A\longrightarrow B,\ (A,\ B\subset \mathbf{R)}$ je funkcia. Mno\v{z}ina \[ G\left( f\right) =\left\{ \left( x,f\left( x\right) \right) \in A\times B\;;\;x\in A\right\} , \]% kde $A\times B$ je kart\'{e}zsky s\'{u}\v{c}in mno\v{z}\'{\i}n $A\ $a $B,$ sa naz\'{y}va \emph{graf} funkcie $f$ $.$ \end{definition} \begin{quote} Z defin\'{\i}cie funkcie vypl\'{y}va, \v{z}e graf funkcie m\'{a} t\'{u} vlastnos\v{t}, \v{z}e ka\v{z}d\'{a} rovnobe\v{z}ka s osou $o_{y}$ pret\'{\i}% na graf najviac v jednom bode. Graf \emph{p\'{a}rnej }funkcie je symetrick\'{y} pod\v{l}a osi $o_{y}$, graf \emph{nep\'{a}rnej }funkcie je symetrick\'{y} pod\v{l}a za\v{c}iatku s\'{u}% radnicovej s\'{u}stavy. \end{quote} \begin{example} Na\v{c}rtnite grafy funkci\'{\i} $f\left( x\right) =\sqrt{16-x^{2}}.$ \end{example} \begin{solution} M\'{a}me: \[ f:\left\langle -4,4\right\rangle \longrightarrow \mathbf{R,}f\left( x\right) =\sqrt{16-x^{2}}\mathbf{.} \]% Plat\'{\i}: \[ \forall x\in D\left( f\right) \Longrightarrow -x\in D\left( f\right) ,\,f\left( -x\right) =\sqrt{16-\left( -x\right) ^{2}}=\sqrt{16-x^{2}}% =f\left( x\right) . \]% Funkcia je p\'{a}rna.$\sqrt{16-x^{2}}$\FRAME{dtbpFX}{4.4996in}{3in}{0pt}{}{}{% Plot}{\special{language "Scientific Word";type "MAPLEPLOT";width 4.4996in;height 3in;depth 0pt;display "USEDEF";plot_snapshots TRUE;mustRecompute FALSE;lastEngine "MuPAD";xmin "-5";xmax "5";xviewmin "-4.008";xviewmax "4.008";yviewmin "-0.003999783219736E0";yviewmax "4.00379572990579";plottype 4;constrained TRUE;numpoints 100;plotstyle "patch";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};function \TEXUX{$\sqrt{16-x^{2}}$};linecolor "blue";linestyle 1;pointstyle "point";linethickness 2;lineAttributes "Solid";var1range "-5,5";num-x-gridlines 100;curveColor "[flat::RGB:0x00000080]";curveStyle "Line";valid_file "T";tempfilename 'HTRF2D03.wmf';tempfile-properties "XPR";}% } \end{solution} \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|} \hline \textbf{% %TCIMACRO{\hyperref{Obsah}{}{}{maindex.tex}}% %BeginExpansion \msihyperref{Obsah}{}{}{maindex.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Obsah kapitoly}{}{}{M2.tex}}% %BeginExpansion \msihyperref{Obsah kapitoly}{}{}{M2.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Predch\'{a}dzaj\'{u}ca str\'{a}nka}{}{}{M22.tex}}% %BeginExpansion \msihyperref{Predch\'{a}dzaj\'{u}ca str\'{a}nka}{}{}{M22.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Nasleduj\'{u}ca str\'{a}nka}{}{}{M24.tex}}% %BeginExpansion \msihyperref{Nasleduj\'{u}ca str\'{a}nka}{}{}{M24.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Ot\'{a}zky}{}{}{O2.tex}}% %BeginExpansion \msihyperref{Ot\'{a}zky}{}{}{O2.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Cvi\v{c}enia}{}{}{C2.tex}}% %BeginExpansion \msihyperref{Cvi\v{c}enia}{}{}{C2.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Index}{}{}{G1.tex}}% %BeginExpansion \msihyperref{Index}{}{}{G1.tex}% %EndExpansion } \\ \hline \end{tabular} \end{center} \rule{6.5in}{0.04in} \textsl{Matematick\'{a} anal\'{y}za I} \section{Funkcie} \end{document}