## 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;

$h =  non_zero_random(-5,5,1);
$k =  random(-6,1,1);

# f(x)=(x+h)^2+k
$b = $h*2;
$c = ($h)**2+$k;

$graph = init_graph(-10,-10,10,10,'axes'=>[0,0],'grid'=>[20,20],'size'=>[400,400]);
$f = FEQ("x**2 + $b x +$c 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 
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) \}
$PAR
END_TEXT

$h1=-$h;

ANS(pc_evaluator([ [interval_cmp("[$h1,infty)"),1],
[interval_cmp("[$h1,infty)", sloppy=>"yes"),0,'Check whether endpoints of your interval should be open or closed.']]));
ANS(pc_evaluator([ [interval_cmp("(-infinity, $h1]"),1],
[interval_cmp("(-infinity, $h1]", 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.