## DESCRIPTION
##  Algebra - Transformation of Graphs 
## ENDDESCRIPTION

## DBsubject(Algebra)
## DBchapter(Transformations of functions and graphs)
## DBsection(Shifts: vertical and horizontal)
## Date(7/17/2022)
## Institution(UWEC)
## Level(2)
## KEYWORDS('Algebra','Transformtions','Graphs','transformations of functions')

#
# First comes some stuff that appears at the beginning of every problem
#

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "answerHints.pl",
  "PGtikz.pl",
  "TikZ_utils.pl",
  "PGcourse.pl",
);



TEXT(beginproblem());
$refreshCachedImages = 1;
#Graph the standard function
$graph=GraphWithTikZ(function=>Formula("x^2"));
#pick offsets
$a=non_zero_random(-3,3);
do {$b=non_zero_random(-3, 3)} until abs($b)!=abs($a);
$c=-$a;

#These are the correct answers
$ans1 = Compute("(x+$c)**2")->with(limits=>[-5,5]);
$ans2 = Compute("x**2+$b")->with(limits=>[-5,5]);

#prepare graph of first correct answer
$graph1 = GraphWithTikZ(function=>$ans1);

# prepare graph of second correct answer
$graph2 =  GraphWithTikZ(function=>$ans2);


BEGIN_TEXT
The graph of \( y= x^2 \) is given below: $BR
\{ image($graph, width=>200, tex_size=>1000) \} $BR
Find a formula for each of the transformations whose graphs
are given below.

$BR
a) 
$BR
\{ image(insertGraph($graph1), width=>200, tex_size=>1000) \} 
$BR
\( y = \) \{ans_rule(30)\}
$BR
b)
$BR
\{ image(insertGraph($graph2), width=>200, tex_size=>1000) \} 
$BR
\( y = \) \{ans_rule(30)\}
END_TEXT

ANS($ans1->cmp()->withPostFilter(AnswerHints(
    [Compute("x**2+$c"),Compute("x**2-$c")]=>"To get a horizontal shift, f(x-h), you must substitute (x-h) IN PARENTHESES for x in the original function.",
     Compute("(x+$a)**2")=>"Be careful of the direction of the shift",
    )));


ANS($ans2->cmp()->withPostFilter(AnswerHints(
    [Compute("(x+$b)**2"),Compute("(x-($b))**2")]=>"To get a vertical shift, f(x)+k, you must add k to the original function.",
     Compute("x**2-($b)")=>"Be careful of the direction of the shift",
    ))
);

ENDDOCUMENT();        # This should be the last executable line in the problem.