calc42-matching.tex

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% BASED ON Hodge-King's
%   IBL Week 4 Day 1 "Derivative Matching Revised"
% DIRECTIONS: typeset twice to get positioning right
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentclass[letterpaper,10pt]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}
\thispagestyle{empty}
\pagestyle{empty}

\newcounter{card}
\newcommand\content[4]{
\begin{tikzpicture}[remember picture, overlay]
\draw (current page.north west)
++({(floor(\arabic{card}/5)+1/2)*1/3*8.5in},{(mod(\arabic{card},5)+1/2)*-1/5*11in}) coordinate (center);
\draw (center) node {
	\begin{tikzpicture}
	\begin{axis}[
		axis equal image=false,
		width=3in, height=2.4in,
		grid=major, axis lines=center,
		xmin=-3.1, xmax=3.1, xtick={-3,...,3},
		ymin=-2.5, ymax=2.5, ytick={-2,...,2},
		major tick length={0},
		samples=299,
		domain=-3:3,
		% #4 = options for this particular graph, eg, xmax, ytick
		#4
		]
		% #2 = list of functions/options to plot = {fn1/op1, fn2/op2, etc}
		% global var \fncolor = color of plot & title
		\foreach \function/\options in {#2}{
			\edef\temp{\noexpand
				\addplot[ultra thick, smooth, \fncolor, \options]{\function};
				}
			\temp
			}
		% #3 = coordinates of open circles = {(x1,y1) (x2,y2), etc}, note no comma btw pts
		\addplot [\fncolor, only marks, very thick, mark=*, mark options={scale=1, fill=white}]
			coordinates{#3};
		% global var \titlef = title = f or f'
		% global var \titlex = relative x position for title = number btw 0, 1
		\node[\fncolor] at (axis description cs: \titlex,0.8) {\huge$\titlef$};
		% #1 = card ID number/letter
		\node at (axis description cs: 0.95,0.05) {\footnotesize#1};
		\end{axis}
		\end{tikzpicture}
		};
	% cut guides
	\foreach \x/\y in {1/1, 1/-1, -1/1, -1/-1}
	\draw[gray] (center) ++(\x*1/2*1/3*8.5in, \y*1/2*1/5*11in)
		edge[-] ++(left:5mm)
		edge[-] ++(right:5mm)
		edge[-] ++(up:5mm)
		edge[-] ++(down:5mm)
		;
	\end{tikzpicture}
	\stepcounter{card}
	}
\newcommand\contentb[2]{\content{#1}{{#2}/{}}{}{restrict y to domain=-2.5:2.5,}}
\newcommand\contentc[2]{\content{#1}{{#2}/{}}{}{
	xmin=-6.3, xmax=6.3, xtick={-6.28319,-3.14159,3.14159, 6.28319},
	xticklabels={$-2\pi$,$-\pi$,$\pi$, $2\pi$},
	ymin=-1.25, ymax=1.25, ytick={-1,-0.5,0.5,1}, 
	domain=-6.2:6.2
	}}

\begin{document}
% FUNCTION CARDS
\def\fncolor{black}
\def\titlef{f}
\def\titlex{0.2}
\contentb 1{2*x-1}
\contentb 2{-2*x+1}
\contentb 3{abs(x)}
\contentb 4{x^2+2*x}
%\contentc 5{sin(deg(x)}
\contentb 5{-x^3/3+0.5}
\contentb 6{x^3-x}
\contentb 7{(x+1)^4-1}
\content 8{ln(x)/domain=0.01:3}{}{samples=300}
\contentb 9{x^3/3+1}
\contentb {10}{x^(-1)}
\contentb {11}{2/(1+2.7182818^(-4*x+4))}
\contentb {12}{(x+1)/abs(x+1)*abs(x+1)^(1/3)}
\contentb {13}{2.7182818^(-x^2)}
\content {14}{0.333*x^3+1/domain=-3:1, x+0.333/{samples=99, domain=1:3}}{}{}
\content {15}{-x^4+4*x^2/{}}{}
	{ymin=-7.5, ymax=7.5, restrict y to domain=-7.5:7.5, ytick={-6,-3,...,6}}

% DERIVATIVE CARDS
\newpage
\def\fncolor{red}
\def\titlef{f'}
\def\titlex{0.8}
\setcounter{card}0
\contentb I2
\contentb E{-2}
\content O{-1/domain=-3:0, 1/domain=0:3}{(0,1) (0,-1)}{samples=2}
\contentb D{2*x+2}
%\contentc F{cos(deg(x))}
\contentb F{-x^2}
\contentb A{3*x^2-1}
\contentb M{4*(x+1)^3}
\content N{{1/x}/domain=0.1:3}{}{samples=30}
\contentb J{x^2}
\contentb K{-1*x^(-2)}
\contentb C{8*2.7182818^(-4*x+4)/(1+2.7182818^(-4*x+4))^2}
\content H{
	{(1/3)*1/(x+1)^2^(1/3)}/domain=-3:-1.01,
	{(1/3)*1/(x+1)^2^(1/3)}/domain=-0.99:3
	}{}{}
\contentb B{-2*x*2.7182818^(-x^2)}
\content G{x^2/domain=-3:1, 1/domain=1:3}{}{}
\content L{-4*x^3+8*x/{}}{}
	{ymin=-7.5, ymax=7.5, restrict y to domain=-7.5:7.5, ytick={-6,-3,...,6}}

% SOLUTIONS
\newpage
\section*{Solutions}
\begin{tabular}{rl}
1 & I %& $\div$
\\ 2 & E %& $\star$
\\ 3 & O %& =
\\ 4 & D %& $\triangle$
\\ 5 & F %& $\infty$
\\ 6 & A %& \&
\\ 7 & M %& @
\\ 8 & N %& $\square$
\\ 9 & J %& \#
\\ 10 & K %& \%
\\ 11 & C %& ?
\\ 12 & H %& !
\\ 13 & B %& $+$
\\ 14 & G %& $\heartsuit$
\\ 15 & L %& $\Rightarrow$
\end{tabular}
\end{document}