Scaling and Translating a Function

Scaling and translating functions

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Complete Code

Download file: ScalingTranslating.pg

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'parserFunction.pl', 'PGcourse.pl');

Preamble

We must load parserFunction.pl so that we can add a named function to the context.

parserFunction(f => 'sin(e * x) + 5.5 * pi * x^2');

$answer = Formula('f(x - 2) + 1');

Setup

The parserFunction method allows us to add a named function to the context. We can define this function however we want, so we chose a function whose formula the students will not guess, whose domain is all real numbers, and which will have no issues during answer evaluation. Once a named function is added to the context, you can use it like you would any other named function.

BEGIN_PGML
A function [`f(x)`] is shifted to the right [`2`] units and up [`1`] unit.  Find
a formula for this shifted function in terms of the function [`f(x)`].

[_]{$answer}{15}
END_PGML

Statement

This is the problem statement in PGML. 
BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.