More complicated drawing using the Fun.pm commands. These are
in the file setGeometry4SubsetsOfR2/ur_geo_4_1.pg
(1 pt) rochesterLibrary/setGeometry4SubsetsOfR2/ur_geo_4_1.pg
For each graph, determine its system of linear inequalities.
1.
A. ![\left\{ \begin{array}{rcl} y & \le & x \cr y & \le & -1 \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/5e/43f490336deaaf12c98d4a754943131.png) B. ![\left\{ \begin{array}{rcl} y & \le & x - 1 \cr y & \ge & -1 \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/6e/e4c5defedb1f789094dbe7000a6ad11.png) C. ![\left\{ \begin{array}{rcl} x & \le & y + 1 \cr y & \ge & -1 \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/59/e81204f75bdb8ac4d99c6b414d7dd71.png) D. ![\left\{ \begin{array}{rcl} y & \le & x - 1 \cr x & \ge & -1 \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/3f/46f58c3dbb45a1b85ec10ea41c48d31.png) E. ![\left\{ \begin{array}{rcl} y & \le & - x + 1 \cr y & \le & -1 \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/c2/c3bcf685898991f83ad0900b186bc91.png) F. None of the above
2.
A. ![\left\{ \begin{array}{rcl} y & \ge & 2 x \cr x & \le & 4 y \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/bc/434033109fb0a374f21812f16c08291.png) B. ![\left\{ \begin{array}{rcl} y & \le & 2 x \cr x & \ge & 0 \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/54/85aa0c0d8a99b129be287f9e9788951.png) C. ![\left\{ \begin{array}{rcl} y & \ge & 2 x \cr x & \ge & 4 y \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/18/1a736c1de17f0bb2bf7a8794d4b0b41.png) D. ![\left\{ \begin{array}{rcl} y & \ge & 4 x \cr x & \ge & 2 y \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/80/5faf9acac79e8d9a8d66885eaaf4a61.png) E. ![\left\{ \begin{array}{rcl} y & \le & 2 x \cr x & \le & 4 y \end{array}\right.](http://webwork.math.rochester.edu/tmp/equations/c5/c0b883bc7df94b16748967926472881.png) F. None of the above
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WARNINGS µ¦å{h
##DESCRIPTION ##KEYWORDS('') ## ##ENDDESCRIPTION
DOCUMENT(); # This should be the first executable line in the problem.
loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGgraphmacros.pl" );
TEXT(beginproblem()); $showPartialCorrectAnswers = 1;
$a = random(2,5,1); $b = random(2,5,1); while ($a == $b) {$b = random(2,5,1);}
$graph1 = init_graph(-3,-3,6,6, 'axes'=>[0,0],'grid'=>[9,9]);
$f3 = FEQ("x/($a) for x in <0,6> using color:black and weight:2"); $f4 = FEQ("$b * x for x in <0,6> using color:black and weight:2");
($f3Ref,$f4Ref) = plot_functions($graph1,$f3,$f4);
$mc1 = new_multiple_choice();
$graph1->fillRegion([1,1,'yellow']);
$mc1->qa(image(insertGraph($graph1),height=>200,width=>200), "\( \left\{ \begin{array}{rcl} y & \le & $b x \cr x & \le & $a y \end{array}\right. \)");
$mc1->extra("\( \left\{ \begin{array}{rcl} y & \ge & $b x \cr x & \le & $a y \end{array}\right. \)", "\( \left\{ \begin{array}{rcl} y & \ge & $b x \cr x & \ge & $a y \end{array}\right. \)", "\( \left\{ \begin{array}{rcl} y & \le & $b x \cr x & \ge & 0 \end{array}\right. \)", "\( \left\{ \begin{array}{rcl} y & \ge & $a x \cr x & \ge & $b y \end{array}\right. \)");
$mc1->makeLast('None of the above');
$c = non_zero_random(-2,2,1);
$graph2 = init_graph(-3,-3,6,6, 'axes'=>[0,0],'grid'=>[9,9]);
$k3 = FEQ("$c for x in <0,6> using color:black and weight:2"); $k4 = FEQ("x+$c for x in <0,6> using color:black and weight:2");
($k3Ref,$k4Ref) = plot_functions($graph2,$k3,$k4);
$fill_point_y = $c + 0.5;
$graph2->fillRegion([1,$fill_point_y,'yellow']);
$mc2 = new_multiple_choice();
$mc2->qa(image(insertGraph($graph2),height=>200,width=>200), "\( \left\{ \begin{array}{rcl} y & \le & x + $c \cr y & \ge & $c \end{array}\right. \)");
$mc2->extra("\( \left\{ \begin{array}{rcl} x & \le & y - $c \cr y & \ge & $c \end{array}\right. \)", "\( \left\{ \begin{array}{rcl} y & \le & x \cr y & \le & $c \end{array}\right. \)", "\( \left\{ \begin{array}{rcl} y & \le & x + $c \cr x & \ge & $c \end{array}\right. \)", "\( \left\{ \begin{array}{rcl} y & \le & - x - $c \cr y & \le & $c \end{array}\right. \)");
$mc2->makeLast('None of the above');
BEGIN_TEXT
For each graph, determine its system of linear inequalities. $BR
1.
\{ $mc2->print_q() \} \{ $mc2->print_a() \}
END_TEXT
ANS(radio_cmp($mc2->correct_ans));
BEGIN_TEXT
2.
\{ $mc1->print_q() \} \{ $mc1->print_a() \}
END_TEXT
ANS(radio_cmp($mc1->correct_ans));
ENDDOCUMENT(); # This should be the last executable line in the problem.
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