# Problem9

Prep Main Page > Web Conference 2 > Sample Problems > Problem 9

This is Library/Rochester/setLimitsRates5Continuity/S02.05.Continuity.PTP01.pg

DOCUMENT();

"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGgraphmacros.pl",
"PGauxiliaryFunctions.pl",
);

TEXT(beginproblem());

\$a=random(1,3,1);
\$b=non_zero_random(-3,0,1);
\$c=random(-3,2,1);
\$m1=non_zero_random(-1,1,0.5);
\$m2= - \$m1;
\$m3=non_zero_random(-1,1,1);
\$m4=non_zero_random(-1,1,1);
@slice = NchooseK(3,3);

@colors = ("blue", "red", "green");
@sc = @colors[@slice];  #scrambled colors
@sa = ('A','B','C')[@slice];

\$f1 = FEQ("sin(10*(x+1)) + \$b for x in [-2,-1) using color:\$sc[0] and weight:2");
\$f2 = FEQ("1 + \$a for x in [-1,-1] using color=\$sc[0] and weight=2");
\$f3 = FEQ("\${m3}/((3*x)**2) + \$b - \${m3}*1/9 for x in (-1,0) using " .
"color=\$sc[0] and weight:2");
\$f4 = FEQ("\${m4}/((3*x)**2) + \$b - \${m4}*1/9 for x in (0,1) using " .
"color=\$sc[0] and weight:2");
\$f5 = FEQ("\$b/5 for x in [1,1] using color=\$sc[0] and weight=2");
\$f6 = FEQ("\${m1}*(x-3)+\$c for x in (1,3] using color=\$sc[0] and weight=2");
\$f7 = FEQ("\${m2}*(x-3)+\$c for x in [3,4] using color=\$sc[0] and weight=2");

\$graph = init_graph(-3,-6,5,6,'axes'=>[0,0],'grid'=>[8,12]);

(\$f1Ref,\$f2Ref,\$f3Ref,\$f4Ref,\$f5Ref,\$f6Ref,\$f7Ref) =
plot_functions(\$graph,\$f1,\$f2,\$f3,\$f4,\$f5,\$f6,\$f7);

TEXT(EV2(<<EOT));
Let \( f \) be the function below.\$PAR
EOT

TEXT(image( insertGraph(\$graph) , height=>200, width=>200));

TEXT(EV2(<<EOT));
\$BR
\$BR

Use \{ helpLink('interval notation')\} to indicate where \( f(x) \)
is continuous.  If it is continuous on more than one interval,
use \$BITALICS U \$EITALICS for union.  You may click on the graph to
make it larger.

\<ans_rule(40)\>
EOT

ANS(interval_cmp("[-2,-1)U(-1,0)U(0,1)U(1,4]"));

ENDDOCUMENT();