ShiftingScalingGraphs
Shifting and Scaling Graphs or Graph Transformations
This PG code shows how to check a student answer that is a shifted and scaled version of a named function.
| PG problem file | Explanation |
|---|---|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "PGgraphmacros.pl", "parserFunction.pl", "unionTables.pl", ); TEXT(beginproblem()); |
Initialization:
We need to include the macros file |
Context("Numeric");
parserFunction("f(x)" => "e^(x/pi)+sin(e*x)");
$answer = Formula("-f(-2x)+1");
foreach my $i (0..1) {
$gr[$i] = init_graph(-5,-5,5,5,axes=>[0,0],grid=>[10,10],size=>[400,400]);
$gr[$i]->lb('reset');
$gr[$i]->lb( new Label(4.5,0.25,'x','black','center','middle'));
$gr[$i]->lb( new Label(0.25,4.5,'y','black','center','middle'));
foreach my $j (1..4) {
$gr[$i]->lb( new Label(-4.5, $j, $j,'black','center','middle'));
$gr[$i]->lb( new Label(-4.5,-$j,-$j,'black','center','middle'));
$gr[$i]->lb( new Label($j, -4.5, $j,'black','center','middle'));
$gr[$i]->lb( new Label(-$j,-4.5,-$j,'black','center','middle'));
}
}
$gr[0]->moveTo(-4, 3);
$gr[0]->lineTo(-2, 3,'blue',3);
$gr[0]->lineTo( 0, 0,'blue',3);
$gr[0]->lineTo( 2, 1,'blue',3);
$gr[1]->moveTo(-1, 0);
$gr[1]->lineTo( 0, 1,'red',3);
$gr[1]->lineTo( 1,-2,'red',3);
$gr[1]->lineTo( 2,-2,'red',3);
foreach my $i (0..1) {
$fig[$i] = image(insertGraph($gr[$i]),width=>400,height=>400,tex_size=>450);
}
|
Setup:
First, we define a named function Second, we graph some piecewise functions for which students will be unable to enter an explicit formula. |
BEGIN_TEXT
The graph of a function \( y = f(x) \) is given in the figure on the left.
The graph of the function \( g(x) \) on the right can be obtained from the
graph of \( f \) by horizontal and vertical scaling and shifting.
What is a formula for \( g(x) \) in terms of \( f(x) \)?
$BR
$BR
\( g(x) \) = \{ ans_rule(20) \}
$BR
$BR
\{
BeginTable().
AlignedRow([$fig[0],$fig[1]]).
TableSpace(5,0).
AlignedRow(["Graph of \( f(x) \)","Shifted and scaled graph \( g(x) \)"]).
EndTable()
\}
END_TEXT
|
Main Text: We use a table to display the graphs nicely. |
$showPartialCorrectAnswers = 1; ANS( $answer->cmp() ); ENDDOCUMENT(); |
Answer Evaluation: Standard. |
- POD documentation: nameOfMacro.pl.html
- PG macro: nameOfMacro.pl
