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<TITLE>Maxima is being fussy</TITLE>
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<P><FONT SIZE=2>Hi,<BR>
<BR>
I have a graph transformation question, that recognizes correct answers most of the time. I was wondering if it could recognize it all of the time.<BR>
<BR>
Example: y = 8 + (x-12)^3<BR>
New graph is vertically compressed by 1/3 and shifted horizontally to the left by 9 units.<BR>
<BR>
A possible solution: 1/3 * (8 + (x -3)^3)<BR>
This solutions was marked wrong as was:<BR>
(8 + (x -3)^3)/3<BR>
<BR>
The solution that was marked correctly was:<BR>
8/3 + ((x-3)^3)/3<BR>
<BR>
I'm not sure why Maxima did not mark the other 2 correctly. Below is the code for the problem.<BR>
<BR>
Also is there something that I'm missing? I am worried that for the algebra response questions that I created students may be marked incorrectly when they are right. <BR>
<BR>
Thanks.<BR>
<BR>
<BR>
<problem><BR>
<script type="loncapa/perl">$origA = &random(5,9,1);<BR>
$origB = &random(10,15,1);<BR>
$origC = &random(16,20,1);<BR>
<BR>
#pick a function<BR>
$index = &random(1,3,1);<BR>
$function = &choose($index, "sqrt($origA-(x-$origB)^2)", "$origA + (x-$origB)^3", "$origA / (x-$origB) + $origC");<BR>
$functionL= &choose($index, "\\sqrt{$origA-(x-$origB)^2}", "$origA + (x-$origB)^3", "\\Large\\frac{$origA}{x-$origB} \\normalsize + $origC");<BR>
<BR>
#set the types of translations<BR>
$temp = &random(1,2,1);<BR>
$compression = &choose($temp,"horizontal ", "vertical ");<BR>
<BR>
$temp = &random(1,2,1);<BR>
$compression = $compression.&choose($temp,"expansion", "compression");<BR>
<BR>
$compressionAmount = &random(2,9,1);<BR>
<BR>
<BR>
$temp = &random(1,2,1);<BR>
$translation = &choose($temp, "horizontal translation", "vertical translation");<BR>
<BR>
$temp = &random(1,2,1)+ ($temp-1)*2;<BR>
$translationDirection = &choose($temp, "left", "right", "up", "down");<BR>
<BR>
do<BR>
{<BR>
$translationAmount = &random(2,9,1);<BR>
}while($compressionAmount==$translationAmount);<BR>
<BR>
<BR>
#set the constants for $a and $b<BR>
if($compression eq "horizontal expansion")<BR>
{<BR>
$a = 1;<BR>
$b = 1/$compressionAmount;<BR>
$texcomp = $compressionAmount;<BR>
}<BR>
elsif($compression eq "horizontal compression")<BR>
{<BR>
$a = 1;<BR>
$b = $compressionAmount;<BR>
$texcomp = "\\frac{1}{$compressionAmount}";<BR>
}<BR>
elsif($compression eq "vertical compression")<BR>
{<BR>
$a = 1/$compressionAmount;<BR>
$b = 1;<BR>
$texcomp = "\\frac{1}{$compressionAmount}";<BR>
}<BR>
else<BR>
{<BR>
$a = $compressionAmount;<BR>
$b = 1;<BR>
$texcomp = $compressionAmount;<BR>
}<BR>
<BR>
<BR>
#set values to $c and $d<BR>
if($translation eq "horizontal translation" && $translationDirection eq "left")<BR>
{<BR>
$c = -1*$translationAmount;<BR>
$d = 0;<BR>
}<BR>
elsif($translation eq "horizontal translation" && $translationDirection eq "right")<BR>
{<BR>
$c = $translationAmount;<BR>
$d = 0;<BR>
}<BR>
elsif($translation eq "vertical translation" && $translationDirection eq "up")<BR>
{<BR>
$c = 0;<BR>
$d = $translationAmount;<BR>
}<BR>
elsif($translation eq "vertical translation" && $translationDirection eq "down")<BR>
{<BR>
$c = 0;<BR>
$d = -1*$translationAmount;<BR>
}<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
<BR>
@args = ($function, $a, $b, $c, $d);</script><startouttext /><p><BR>
What is the equation of <m eval="on"> $ y= $functionL$ </m> after a<BR>
$compression by a factor of <m eval="on">$ $texcomp $</m> and<BR>
$translation $translationAmount units $translationDirection?<BR>
</p><BR>
Instructions: <br /><BR>
<ul><BR>
<li>Use * for multiplication, / for division, ^ for exponent and brackets</li><BR>
<li>For example to represent <m>$y=\Large\frac{(x^3-4)^5}{2}$</m>you would type: ((x^3-4)^5)/2</li><BR>
<li>If you enter a formula, double check your formula by clicking on the pencil icon to get a<BR>
different representation of your formula </li><BR>
<li>Another example to represent <m>$\sqrt{x^2+3} - 5$</m> you would type: sqrt(x^2 + 3) - 5</li><BR>
</ul><BR>
<BR>
<br /><BR>
<br /><BR>
<BR>
<BR>
Answer: <m>$y =$</m><endouttext /><BR>
<mathresponse cas="maxima" args="@args" id="11"><BR>
<answer>f(x) := LONCAPALIST[1];<BR>
a:LONCAPALIST[2];<BR>
b:LONCAPALIST[3];<BR>
c:LONCAPALIST[4];<BR>
d:LONCAPALIST[5];<BR>
g(x) := LONCAPALIST[2]*f(LONCAPALIST[3]*(x-LONCAPALIST[4]))+LONCAPALIST[5];<BR>
is(trigsimp(trigreduce(RESPONSE[1]-g(x)))=0);</answer><BR>
<textline readonly="no" /><BR>
<BR>
</mathresponse><BR>
</problem><BR>
<BR>
<BR>
<BR>
</FONT>
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