<html><head></head><body><div style="color:#000; background-color:#fff; font-family:Helvetica Neue-Light, Helvetica Neue Light, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:16px"><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400">Hi,</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400"><br></div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400" dir="ltr">I am not sure if you are inclined to pick up tikz.</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400"><br></div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400">I commented out a part of the options at the beginning - not sure why they did not work and no time to pursue that.</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400"><br></div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400">I added one line by modifying the line that  plots f(x) to give the inverse graph.</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400"><br></div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400">%%%%%%%%%%%%%%%</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49400">\documentclass{standalone}</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49401">\usepackage{tikz}</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49402"><br id="yui_3_16_0_ym19_1_1476768290147_49403"></div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49404">\begin{document}</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49405">\definecolor{qqqqff}{rgb}{0.,0.,1.}</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49406">\definecolor{ffqqqq}{rgb}{1.,0.,0.}</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49407">\begin{tikzpicture}%[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49408">\draw[->,color=black] (-7.025,0.) -- (14.53,0.);</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49409">\foreach \x in {-6.,-4.,-2.,2.,4.,6.,8.,10.,12.,14.}</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49410">\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49411">\draw[->,color=black] (0.,-6.625) -- (0.,7.865);</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49412">\foreach \y in {-6.,-4.,-2.,2.,4.,6.}</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49413">\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49414">\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49415">\clip(-7.025,-6.625) rectangle (14.53,7.865);</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49416">\draw[line width=1.2pt,color=ffqqqq,smooth,samples=100,domain=-3.025000000000002:6.530000000000006] plot(\x,{(\x)^(3.0)+4.0});</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49417">\draw[line width=1.2pt,color=ffqqqq,smooth,samples=100,domain=-3.025000000000002:6.530000000000006] plot({(\x)^(3.0)+4.0},\x); %% swapping x and y coordinates gives inverse graph</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49418">\draw [color=ffqqqq](1.345,6.065) node[anchor=north west] {$f(x)=x^3 + 4$};</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49419">\draw [color=qqqqff](1.66,-1.045) node[anchor=north west] {$f^{-1}(x) = \sqrt[3]{x-4}$};</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49420">\draw[line width=1.2pt,color=qqqqff, smooth,samples=100,domain=-3.07000000000001:6.57500000000001] plot[parametric] function{6.123233995736766E-17*(t+0.0)+t**(3.0)+4.0,t+0.0-6.123233995736766E-17*(t**(3.0)+4.0)-0.0};</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49421">\end{tikzpicture}</div><div style="margin-top: 0px; margin-bottom: 0px;" id="yui_3_16_0_ym19_1_1476768290147_49422">\end{document}</div><div>





















</div><div style="margin-top: 0px; margin-bottom: 0px;" dir="ltr" id="yui_3_16_0_ym19_1_1476768290147_49423"><br id="yui_3_16_0_ym19_1_1476768290147_49424"></div><div></div><div> </div><div class="signature" id="yui_3_16_0_ym19_1_1476768290147_49345">@-->------ <div id="yui_3_16_0_ym19_1_1476768290147_49346">May you be happy and well! </div><div id="yui_3_16_0_ym19_1_1476768290147_49347">B.A. </div><div id="yui_3_16_0_ym19_1_1476768290147_49348">------<--@</div></div> <div class="qtdSeparateBR"><br><br></div><div class="yahoo_quoted" style="display: block;"> <div style="font-family: Helvetica Neue-Light, Helvetica Neue Light, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div dir="ltr"><font size="2" face="Arial"> On Tuesday, 18 October 2016, 6:20, Tim Brophy <timbrophy@mac.com> wrote:<br></font></div>  <br><br> <div class="y_msg_container">Thanks everybody.<br clear="none"><br clear="none">As a temporary solution I have simply exported the graphic as a pdf file and included it in beamer. <br clear="none"><br clear="none">I downloaded gnuplot and put it in my Applications folder. This may not be the correct thing to do. I got it from Sourceforge and don’t know if it is even the correct version for the Mac.<br clear="none"><br clear="none"><br clear="none">> On 17 Oct 2016, at 22:24, Michael Sharpe <<a shape="rect" ymailto="mailto:msharpe@ucsd.edu" href="mailto:msharpe@ucsd.edu">msharpe@ucsd.edu</a>> wrote:<br clear="none">> <br clear="none">> <br clear="none">>> On Oct 17, 2016, at 2:01 PM, Tim Brophy <<a shape="rect" ymailto="mailto:timbrophy@mac.com" href="mailto:timbrophy@mac.com">timbrophy@mac.com</a>> wrote:<br clear="none">>> <br clear="none">>> {6.123233995736766E-17*(t+0.0)+t**(3.0)+4.0,t+0.0-6.123233995736766E-17*(t**(3.0)+4.0)-0.0}<br clear="none">> <br clear="none">> <br clear="none">> I don't believe gnuplot is really needed, and you received that warning because of the overly complex way your parametric function was specified. Instead of the above, try<br clear="none">> <br clear="none">> {t^3+4,t} <br clear="none">> <br clear="none">> so that that Tikz doesn't think that non-integer powers are called for.<br clear="none">> <br clear="none">> Michael<br clear="none">> ----------- Please Consult the Following Before Posting -----------<br clear="none">> TeX FAQ: <a shape="rect" href="http://www.tex.ac.uk/faq" target="_blank">http://www.tex.ac.uk/faq</a><br clear="none">> List Reminders and Etiquette: <a shape="rect" href="https://www.esm.psu.edu/~gray/tex/" target="_blank">https://www.esm.psu.edu/~gray/tex/</a><br clear="none">> List Archives: <a shape="rect" href="http://dir.gmane.org/gmane.comp.tex.macosx" target="_blank">http://dir.gmane.org/gmane.comp.tex.macosx</a><br clear="none">>                <a shape="rect" href="https://email.esm.psu.edu/pipermail/macosx-tex/" target="_blank">https://email.esm.psu.edu/pipermail/macosx-tex/</a><br clear="none">> TeX on Mac OS X Website: <a shape="rect" href="http://mactex-wiki.tug.org/" target="_blank">http://mactex-wiki.tug.org/</a><br clear="none">> List Info: <a shape="rect" href="https://email.esm.psu.edu/mailman/listinfo/macosx-tex" target="_blank">https://email.esm.psu.edu/mailman/listinfo/macosx-tex</a><div class="yqt4232105105" id="yqtfd61492"><br clear="none"><br clear="none"><br clear="none">----------- Please Consult the Following Before Posting -----------<br clear="none">TeX FAQ: <a shape="rect" href="http://www.tex.ac.uk/faq" target="_blank">http://www.tex.ac.uk/faq</a><br clear="none">List Reminders and Etiquette: <a shape="rect" href="https://www.esm.psu.edu/~gray/tex/" target="_blank">https://www.esm.psu.edu/~gray/tex/</a><br clear="none">List Archives: <a shape="rect" href="http://dir.gmane.org/gmane.comp.tex.macosx" target="_blank">http://dir.gmane.org/gmane.comp.tex.macosx</a><br clear="none">                <a shape="rect" href="https://email.esm.psu.edu/pipermail/macosx-tex/" target="_blank">https://email.esm.psu.edu/pipermail/macosx-tex/</a><br clear="none">TeX on Mac OS X Website: <a shape="rect" href="http://mactex-wiki.tug.org/" target="_blank">http://mactex-wiki.tug.org/</a><br clear="none">List Info: <a shape="rect" href="https://email.esm.psu.edu/mailman/listinfo/macosx-tex" target="_blank">https://email.esm.psu.edu/mailman/listinfo/macosx-tex</a><br clear="none"></div><br><br></div>  </div> </div>  </div></div></body></html>