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| 1 : | jj | 145 | ##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 : |
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