## WeBWorK Problems

### Extra information appearing in graph

by James Morski -
Number of replies: 2

I have run in to the following issue. I have created dynamicimages for the below problem. Each of the exponential portions renders correctly, but some extra information gets added to the graph in some cases (see attached).

When I re-seed, the issue sometimes appears and sometimes does not. I know that I could alter the domain for the functions, but this doesn't really solve the issue. I have also messed around with different steps in the graph (using
($gr->fn)[0]->steps(2000);), but this doesn't fix it either. Here is my code. Can anybody view a problem? Thanks! James ## DESCRIPTION ## Algebra, Exponential functions ## ENDESCRIPTION ## DBsubject() ## DBchapter() ## DBsection() ## Date(06/26/2017) ## Institution(Colorado Community College System) ## Author(James Morski) ## Static(1) ## MO(1) ## KEYWORDS('algebra','exponential functions') ########################### # Initialization DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "PGchoicemacros.pl", "parserAssignment.pl", "AnswerFormatHelp.pl", "PGML.pl", "PGgraphmacros.pl", "parserPopUp.pl", "PGcourse.pl", "contextLimitedPoint.pl", ); TEXT(beginproblem());$showPartialCorrectAnswers = 1;

##########################
# Setup

$a=random(-5,-2,1);$b=random(.15,.85,.1);
$c=random(1,5,1);$d=random(1,5,1);

$gr = init_graph(-10,-10,10,10, axes=>[0,0], grid=>[10,10], size=>[600,600] );$gr1 = init_graph(-10,-10,10,10,
axes=>[0,0],
grid=>[10,10],
size=>[600,600]
);

$gr2 = init_graph(-10,-10,10,10, axes=>[0,0], grid=>[10,10], size=>[600,600] );$gr3 = init_graph(-10,-10,10,10,
axes=>[0,0],
grid=>[10,10],
size=>[600,600]
);

$gr4 = init_graph(-10,-10,10,10, axes=>[0,0], grid=>[10,10], size=>[600,600] ); add_functions($gr, "($a($b)^x) for x in <-10,10>" .
" using color:blue and weight:2");

add_functions($gr1, "($a($b)^(x+$c)-$d) for x in <-10,10>" . " using color:blue and weight:2"); add_functions($gr2, "(-$a($b)^(x)-$c) for x in <-10,10>" . " using color:blue and weight:2"); add_functions($gr3, "($a($b)^(x-$d)-$c) for x in <-10,10>" .
" using color:blue and weight:2");

add_functions($gr4, "($a($b)^(x+$d)+$c) for x in <-10,10>" . " using color:blue and weight:2"); Context("Numeric");$popup1 = PopUp(
["?","A","B", "C", "D"], "C",
);

$popup2 = PopUp( ["?","x","y"], "y", );$fun=("$a($b)^x");

$ans1=("$a($b)^(x+$d)+$c");$ans2 = ("$c"); ################################# # Main text BEGIN_PGML The graph of f(x)=[$fun] is given below (click on graph to enlarge):

>>[@ image(insertGraph($gr), width=>300, height=>300), @]*<< Let g(x) be the transformation of f(x) up [$c] units and left [$d] units. Which of the following graphs represents the graph of g(x)? [_________________]{$popup1}

>>A. [@ image(insertGraph($gr1), width=>200, height=>200), @]* B. [@ image(insertGraph($gr2), width=>200, height=>200), @]* <<

>>C. [@ image(insertGraph($gr4), width=>200, height=>200), @]* D. [@ image(insertGraph($gr3), width=>200, height=>200), @]* <<

What is the equation for g(x)?

>>g(x)= [_________________]{$ans1} [@ AnswerFormatHelp("formulas") @]*<< What is the horizontal asymptote of g(x)? Enter the equation of a line. >>[_________________]{$popup2}=[_________________]{$ans2}<< END_PGML ################################# # Solution #BEGIN_PGML_SOLUTION #Solution explanation goes here. #END_PGML_SOLUTION COMMENT('Uses PGML.'); ENDDOCUMENT(); In reply to James Morski ### Re: Extra information appearing in graph by Davide Cervone - The issue is probably that the values of the equations have huge magnitudes near the left of the graph. For example, with$a = -5, $b = .15;$c = 5, and $d = 5, some of the graphs have magnitudes on the order of 10^13. I don't know how the graphing library deals with values on that order, but I suspect there are numeric problems associated with that. One solution would be only to use x values that produce reasonable sized y values. E.g., $m = ln(-15/$a)/ln($b);
add_functions($gr, "($a($b)^x) for x in <$m,10>" .
" using color:blue and weight:2");

$m = ln(($d-15)/$a)/ln($b)-$c; add_functions($gr1, "($a($b)^(x+$c)-$d) for x in <$m,10>" . " using color:blue and weight:2");$m = ln(-($c+15)/$a)/ln($b); add_functions($gr2, "(-$a($b)^(x)-$c) for x in <$m,10>" .
" using color:blue and weight:2");

$m = ln(($c-15)/$a)/ln($b)+$d; add_functions($gr3, "($a($b)^(x-$d)-$c) for x in <$m,10>" . " using color:blue and weight:2");$m = ln((-$c-15)/$a)/ln($b)-$d;
add_functions($gr4, "($a($b)^(x+$d)+$c) for x in <$m,10>" .
" using color:blue and weight:2");

(I didn't check the math for \$m carefully, so you might want to double check that.)