## DESCRIPTION
## Algebra
## ENDDESCRIPTION

## KEYWORDS('function' 'graph' 'slope')
## Tagged by tda2d

## DBsubject('Algebra')
## DBchapter('Functions')
## DBsection('Average Rate of Change: Increasing and Decreasing Functions')
## Date('')
## Author('')
## Institution('Rochester')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

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

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"PGgraphmacros.pl",
"extraAnswerEvaluators.pl",
"PGasu.pl",
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = random(1,5,1);
$b = random(-5,0,1);

$graph = init_graph(-10,-10,10,10,'axes'=>[0,0],'grid'=>[20,20],'size'=>[400,400]);
$f = FEQ("abs(x-$a)+abs(x+$a)+$b for x in <-10,10> using color:green and weight:2");

plot_functions($graph,$f);

BEGIN_TEXT
$BR

Consider the function whose graph is sketched:
$BR \{ image(insertGraph($graph), width=>200, height=>200) \} $BR
Find the intervals over which the function is strictly increasing or 
strictly decreasing. 
Express your answer in \{ helpLink('interval notation')\}.
$BR $BR 
The interval over which the function is strictly increasing: \{ans_rule(35) \}
$BR
The interval over which the function is strictly decreasing: \{ans_rule(35) \}
END_TEXT

#ANS(interval_cmp("[$a,infty)", sloppy=>"yes"));
ANS(pc_evaluator([ [interval_cmp("[$a,infty)"),1],
[interval_cmp("[$a,infty)", sloppy=>"yes"),0,'Check whether endpoints of your interval should be open or closed.']]));
ANS(pc_evaluator([ [interval_cmp("(-infinity, -$a]"),1],
[interval_cmp("(-infinity, -$a]", sloppy=>"yes"),0,'Check whether endpoints of your interval should be open or closed.']]));



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