GraphsInTables
Putting Graphs into Tables
This PG code shows how to put graphs into tables so that they will be displayed compactly and a proper size in both HTML and TeX modes.
- Example 1: Putting a text block and a graph side-by-side using ColumnTable from unionTables.pl
- Example 4: Displaying a narrow text block and an array of graphs side-by-side using ColumnTable and BeginTable from unionTables.pl
Example 1: Putting a text block and a graph side-by-side using ColumnTable from unionTables.pl
PG problem file | Explanation |
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DOCUMENT(); loadMacros( "PGstandard.pl", "PGgraphmacros.pl", "MathObjects.pl", "unionTables.pl", # or "PGunion.pl", ); TEXT(beginproblem()); $refreshCachedImages=1; |
Initialization:
Be sure to load |
Context("Numeric"); $a = random(2,3,1); # -$a is the left x-intercept $b = random(2,4,2); # $b is the right x-intercept $c = random(1,4,1); # -$c is the y-intercept $k = $c/($a * $b); $A = $k; $B = $k*($a - $b); $C = -($c); $gr = init_graph(-5,-5,5,5,axes=>[0,0],grid=>[10,10]); add_functions($gr, "$A*x**2+$B*x+$C for x in <-5,5> using color:blue and weight:2"); $gr -> lb(new Label ( 4.5,0,'x','black','left','bottom')); $gr -> lb(new Label ( 0.25,8.5,'y','black','left','bottom')); $gr -> lb(new Label ( 0.25,$c,'y = f(x)','black','left','bottom')); |
Setup:
Generate a graph to be included in the main text. This graph is a parabola opening up with roots |
Context()->texStrings; BEGIN_TEXT \{ ColumnTable( "Use the graph to find the missing values. There may be more than one correct answer, in which case you should enter your answers as a comma separated list. If there are no correct answers, enter ${BITALIC}NONE.${EITALIC}". $BR. $BR. "(a) \( f(0) = \) ". ans_rule(7). $BR. $BR. "(b) \( f \big( \) ".ans_rule(7)." \( \big) = 0 \). ", # comma! image(insertGraph($gr), width=>400, height=>400, tex_size=>700). $BR.$BCENTER. "(Click on graph to enlarge)". $ECENTER, # comma! indent => 0, separation => 30, valign => "TOP" ) \} END_TEXT Context()->normalStrings; |
Main Text:
We use Using ColumnTable has two main advantages.
|
$showPartialCorrectAnswers = 1; ANS( List(-$c)->cmp() ); ANS( List(-$a,$b)->cmp() ); ENDDOCUMENT(); |
Answer Evaluation:
Since there may be multiple answers, we use |
Example 4: Displaying a narrow text block and an array of graphs side-by-side using ColumnTable and BeginTable from unionTables.pl
PG problem file | Explanation |
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loadMacros( "PGstandard.pl", "PGchoicemacros.pl", "PGgraphmacros.pl", "unionTables.pl", ); TEXT(beginproblem()); # standard preamble to each problem. $refreshCachedImages=1; |
Initialization:
Be sure to load |
#################################### # Create blank canvases with labels # foreach $j (0..5) { $graph[$j] = init_graph(-10,-10,10,10,'axes'=>[0,0],'ticks'=>[10,10],'size'=>[400,400]); $graph[$j]->lb('reset'); foreach ($i = 1; $i <= 4; $i++) { $graph[$j]->lb(new Label(2*$i,-.1,2*$i,'black','center','top')); $graph[$j]->lb(new Label(-2*$i,-.1,-2*$i,'black','center','top')); $graph[$j]->lb(new Label(-.1,2*$i,2*$i,'black','right','middle')); $graph[$j]->lb(new Label(-.1,-2*$i,-2*$i,'black','right','middle')); } $graph[$j]->lb(new Label(9.8,-0.1,"x",'black','right','top')); $graph[$j]->lb(new Label(-.1,9.8,"y",'black','right','top')); } ######################################### # Manually add functions to the canvases # $f[0] = "\frac{-1}{x-5}-1"; plot_functions($graph[0], "-1/(x-5)-1 for x in <-10,4.99> using color:blue and weight:2", "-1/(x-5)-1 for x in <5.01,10> using color:blue and weight:2", ); # vertical asymptote $graph[0]->moveTo(5,-10); $graph[0]->lineTo(5,10,'black',1,'dashed'); # horizontal asymptote $graph[0]->moveTo(-10,-1); $graph[0]->lineTo(10,-1,'black',1,'dashed'); $f[1] = "\frac{x-2}{(x+1)(x-3)}"; plot_functions($graph[1], "(x-2)/((x+1)*(x-3)) for x in <-10,-1.01> using color:blue and weight:2", "(x-2)/((x+1)*(x-3)) for x in <-0.99,2.99> using color:blue and weight:2", "(x-2)/((x+1)*(x-3)) for x in <3.01,10> using color:blue and weight:2", ); # vertical asymptote $graph[1]->moveTo(-1,-10); $graph[1]->lineTo(-1,10,'black',1,'dashed'); # vertical asymptote $graph[1]->moveTo(3,-10); $graph[1]->lineTo(3,10,'black',1,'dashed'); $f[2] = "\frac{2x+4}{x-1}"; plot_functions($graph[2], "(2x+4)/(x-1) for x in <-10,0.99> using color:blue and weight:2", "(2x+4)/(x-1) for x in <1.01,10> using color:blue and weight:2", ); # vertical asymptote $graph[2]->moveTo(1,-10); $graph[2]->lineTo(1,10,'black',1,'dashed'); # horizontal asymptote $graph[2]->moveTo(-10,2); $graph[2]->lineTo(10,2,'black',1,'dashed'); $f[3] = "\frac{1}{x+1} + \frac{1}{x-3}"; plot_functions($graph[3], "1/(x+1)+1/(x-3) for x in <-10,-1.01> using color:blue and weight:2", "1/(x+1)+1/(x-3) for x in <-0.99,2.99> using color:blue and weight:2", "1/(x+1)+1/(x-3) for x in <3.01,10> using color:blue and weight:2", ); # vertical asymptote $graph[3]->moveTo(-1,-10); $graph[3]->lineTo(-1,10,'black',1,'dashed'); # vertical asymptote $graph[3]->moveTo(3,-10); $graph[3]->lineTo(3,10,'black',1,'dashed'); $f[4] = "\frac{1-x^2}{x-2}+3"; plot_functions($graph[4], "(1-x^2)/(x-2)+3 for x in <-10,1.99> using color:blue and weight:2", "(1-x^2)/(x-2)+3 for x in <2.01,10> using color:blue and weight:2", ); # vertical asymptote $graph[4]->moveTo(2,-10); $graph[4]->lineTo(2,10,'black',1,'dashed'); $f[5] = "\frac{1-4x}{2x+2}"; plot_functions($graph[5], "(1-4x)/(2x+2) for x in <-10,-1.01> using color:blue and weight:2", "(1-4x)/(2x+2) for x in <-0.99,10> using color:blue and weight:2", ); # vertical asymptote $graph[5]->moveTo(-1,-10); $graph[5]->lineTo(-1,10,'black',1,'dashed'); # horizontal asymptote $graph[5]->moveTo(-10,-2); $graph[5]->lineTo(10,-2,'black',1,'dashed'); ############################################### # Create figures that can be inserted directly # foreach $j (0..5) { $fig[$j] = image(insertGraph($graph[$j]), width => 200, height => 200, tex_size => 310); } ############################################### # Shuffle the figures # @perm = shuffle(6); @inv = invert(@perm); @fig = @fig[@perm]; @letter = ("A","B","C","D","E","F"); |
Setup: Generate a number of graphs to be included in the main text. Then, near the bottom, shuffle the graphs. |
BEGIN_TEXT \{ ColumnTable( "Without a calculator, match each function with its graph A-F by finding the zeros, asymptotes, and end behavior for each function.". $BR.$BR.pop_up_list(["?",@letter]).$SPACE."\( \displaystyle y = $f[0] \)". $BR.$BR.pop_up_list(["?",@letter]).$SPACE."\( \displaystyle y = $f[1] \)". $BR.$BR.pop_up_list(["?",@letter]).$SPACE."\( \displaystyle y = $f[2] \)". $BR.$BR.pop_up_list(["?",@letter]).$SPACE."\( \displaystyle y = $f[3] \)". $BR.$BR.pop_up_list(["?",@letter]).$SPACE."\( \displaystyle y = $f[4] \)". $BR.$BR.pop_up_list(["?",@letter]).$SPACE."\( \displaystyle y = $f[5] \)", # comma! BeginTable(). AlignedRow([$fig[0],$fig[1],$fig[2]]). TableSpace(5,0). AlignedRow(["A","B","C"]). TableSpace(25,6). AlignedRow([$fig[3],$fig[4],$fig[5]]). TableSpace(5,0). AlignedRow(["D","E","F"]). EndTable(). $BR.$BCENTER."(Click on a graph to enlarge it)".$ECENTER, # comma! indent => 0, separation => 10, valign => "TOP" ) \} END_TEXT |
Main Text:
We use |
install_problem_grader(~~&std_problem_grader); $showPartialCorrectAnswers = 0; foreach $j (0..5) { ANS( str_cmp($letter[$inv[$j]]) ); } ENDDOCUMENT(); |
Answer Evaluation:
To keep students from guessing, we use the all-or-nothing grader |
\{ imageRow( ["graph1.png","graph2.png"], ["A","B"], width=>250, height=>250, tex_size=>450 ) \} \{ imageRow( ["g1.png","g2.png","g3.png"], ["A","B","C"], width=>200, height=>200, tex_size=>310 ) \} \{ imageRow( ["g1.png","g2.png","g3.png","g4.png"], ["A","B","C","D"], width=>150, height=>150, tex_size=>200 ) \}
The imageRow
function displays multiple images in a row. Its first argument is a list of image files and its second argument ["A","B"]
is a list of caption names. The double quotes in caption names are necessary, for example, to prevent the string "E" from being interpreted as E = 2.718...