Return to Function_Plot_Response_Evaluation_Rule.tex CVS log

Up to [LON-CAPA] / loncom / html / adm / help / tex

Annotation of loncom/html/adm/help/tex/Function_Plot_Response_Evaluation_Rule.tex, revision 1.7

1.1       www         1: \label{Function_Plot_Response_Evaluation_Rule}
                      2: 
1.5       www         3: Overview - This box is used to create a rule that determines whether or not a submitted graph is correct.  In general, it takes the form of testing the function, its integral, or its first or second derivative over a given set of x-values.  The test can be to see if it equals, is greater than, or less than a specified value.  Anywhere a number is needed, a variable can also be used.  (Skip to the bottom for examples of rules.)
1.1       www         4: 
1.5       www         5: \begin{itemize}
1.7     ! raeburn     6: \item ``Index/Name'' - This is an internal label for the rule.  Something must be entered here, and it must be different for each rule.  This same value will be used to add a conditional hint.
1.1       www         7: 
1.7     ! raeburn     8: \item ``Function'' - This determines what the server will be testing.  For instance, choose `First derivative' causes the server to evaluate the derivative of the entered answer over the given domain.
1.1       www         9: 
1.5       www        10: \item ``Initial x-value'' and ``Initial x-value label'' - A value must be entered for one of these.  Either choose a numerical value for x (the first option), or choose the beginning of the submitted answer, the end, or a previously chosen named point (see below).
1.1       www        11: 
1.5       www        12: \item ``Final x-value'' and ``Final x-value label'' - This determines the end of the domain over which the rule examines.  To test only a single point (the initial value), leave these blank.  If a label is entered, such as `positive', the point at which the rule fails will be given this special label.  This label can then be used in subsequent rules as an 'Initial x-value label'.
1.1       www        13: 
1.5       www        14: \item ``Minimum length for range'' - This tests that the difference between the initial and final x-values are at least a certain length apart.  This is only useful if there is at least one label.
1.1       www        15: 
1.5       www        16: \item ``Maximum length for range'' - This tests that the difference between the initial and final x-values are at most a certain length apart.  This is only useful if there is at least one label.
1.1       www        17: 
1.5       www        18: \item ``Relationship''  - The heart of the rule.  This choice determines whether the chosen `Function' is greater than, less than, equal to, etc. a certain `Value'.
1.1       www        19: 
1.7     ! raeburn    20: \item ``Value'' - Enter the number you wish to compare to.  It is also possible to choose `not defined', in the event the answer should not have a value for the given domain. Within the value argument, the function itself can be evaluated using \&fpr\_f(), its derivative using \&fpr\_dfdx(), and its second derivative using \&fpr\_d2fdx2(). This allows for a comparison of two points on the graph.  The value of a previously defined label can be retrieved using the function \&fpr\_val(), e.g., \&fpr\_val(`positive'). Previous defined values from script blocks can also be retrieved as normal variables, e.g., \$x.
1.1       www        21: 
1.5       www        22: \item ``Percent error'' - This allows for a margin of error in the y-direction.  For instance, if the rule requires that the derivative be equal to 5, the server will accept values close enough to 5 that are within the percent error defined here. Note: Choosing 10\% would not mean that the answer is correct as long as it is within the range 4.5-5.5.  Instead, the percent corresponds to the total size of the graph.  For the function itself, the `percent error' is multiplied by the ymax-ymin; for the first derivative, it's multiplied by (ymax-ymin)/(xmax-xmin); for the second derivative, it's multiplied by (ymax-ymin)/(xmax-xmin)$^2$; and for the integral, it's multiplied by (ymax-ymin)*(xmax-xmin).
                     23: \end{itemize}
1.1       www        24: 
1.5       www        25: The figure below shows some examples of rules.
1.1       www        26: 
1.6       lira       27: \includegraphics[height=1\paperwidth]{FPRexamples}
1.5       www        28: 
                     29: \begin{enumerate}
                     30: 
                     31: \item Checks that the derivative at $x=3$ is negative.
                     32: 
                     33: \item Checks that the second derivative at $x=$\$time1 is $0$.
                     34: 
1.7     ! raeburn    35: \item Checks that the value of the function $>7$ from ``Start of Graph'' to $x=5$.
1.5       www        36: 
                     37: \item Checks that the function is $0$ from $x=0$ until the function is no longer $0$, labeling this new point `notzero'.
                     38: 
                     39: \item Checks that the first derivative is positive between the point `notzero' and the end of the graph.
                     40: 
                     41: \item Checks to see that the value of the function at $x=4$ is the same as the value of the function at \$time2. The Value here is \&fpr\_f(\$time2).
                     42: 
                     43: \item Checks that the value of the function at point `notzero' is equal to the value of the function at $x=$ \$time3.  The Value here is \&fpr\_f(\&fpr\_val(`notzero')).
                     44: 
                     45: \end{enumerate}