View of /trunk/NationalProblemLibrary/Rochester/setAlgebra28ExpFunctions/pexp.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('logarithms,exponentials','exponential growth,decay')
    3 ##TYPE('word problem')
    4 ##ENDDESCRIPTION
    5 
    6 DOCUMENT();        # This should be the first executable line in the problem.
    7 
    8 loadMacros(
    9 "PG.pl",
   10 "PGbasicmacros.pl",
   11 "PGchoicemacros.pl",
   12 "PGanswermacros.pl",
   13 "PGauxiliaryFunctions.pl"
   14 );
   15 
   16 TEXT(beginproblem());
   17 $showPartialCorrectAnswers = 1;
   18 
   19 $e = random(2,9,1);
   20 
   21 $a1 = random(1,9,1);
   22 $ag = random(0,1,1);
   23 if ($ag == 0) {
   24   $a2 = 'downward';
   25   $ans_a = "$e^x - $a1";
   26   }
   27 if ($ag == 1) {
   28   $a2 = 'upward';
   29   $ans_a = "$e^x + $a1";
   30   }
   31 
   32 $b1 = random(1,9,1);
   33 $bg = random(0,1,1);
   34 if ($bg == 0) {
   35   $b2 = 'right';
   36   $ans_b = "$e^(x - $b1)";
   37   }
   38 if ($bg == 1) {
   39   $b2 = 'left';
   40   $ans_b = "$e^(x + $b1)";
   41   }
   42 
   43 $cg = random(0,2,1);
   44 if ($cg == 0) {
   45   $c1 = 'x-axis';
   46   $ans_c = "-$e^x";
   47   }
   48 if ($cg == 1) {
   49   $c1 = 'y-axis';
   50   $ans_c = "$e^(-x)";
   51   }
   52 if ($cg == 2) {
   53   $c1 = 'x-axis and the y-axis';
   54   $ans_c = "-$e^(-x)";
   55   }
   56 
   57 #$d1 = non_zero_random(-4,4,1);
   58 #$temp = 2 * $d1;
   59 #$dg = random(0,1,1);
   60 #if ($dg == 0) {
   61 #  $d2 = 'x';
   62 #  $ans_d = "$e**($temp-x)";
   63 #  }
   64 #if ($dg == 1) {
   65 #  $d2 = 'y';
   66 #  $ans_d = "$temp-$e**x";
   67 #  }
   68 
   69 TEXT(EV2(<<EOT));
   70 Starting with the graph of \( f(x) = $e^{x} \), write the equation of the graph that results from
   71 $BR $BR (a) shifting \( f(x) \) $a1 units $a2.  \( y = \) \{ans_rule(20) \}
   72 $BR $BR (b) shifting \( f(x) \) $b1 units to the $b2.  \( y = \) \{ans_rule(20) \}
   73 $BR $BR (c) reflecting \( f(x) \) about the $c1.  \( y = \) \{ans_rule(20) \}
   74 EOT
   75 #$PAR (d) reflecting \( f(x) \) about the line $d2 = $d1.  \( y = \) \{ans_rule(20) \}
   76 
   77 
   78 
   79 ANS(fun_cmp($ans_a));
   80 ANS(fun_cmp($ans_b));
   81 ANS(fun_cmp($ans_c));
   82 #ANS(fun_cmp($ans_d));
   83 
   84 ENDDOCUMENT();        # This should be the last executable line in the problem.
   85