View of /trunk/NationalProblemLibrary/Rochester/setAlgebra28ExpFunctions/srw4_1_29.pg

    1 #DESCRIPTION
    2 ##  Algebra problem: Exponential Functions
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('algebra', 'expeonential function')
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros(
   10 "PG.pl",
   11 "PGbasicmacros.pl",
   12 "PGchoicemacros.pl",
   13 "PGanswermacros.pl",
   14 "PGauxiliaryFunctions.pl"
   15 );
   16 
   17 TEXT(beginproblem());
   18 $showPartialCorrectAnswers = 0;
   19 install_problem_grader(~~&std_problem_grader);
   20 
   21 $a=random(3,9,1);
   22 
   23 BEGIN_TEXT
   24 The graph of the function
   25 \( f(x)=e^{-x}-$a \)
   26 can be obtained from the graph of
   27 \( g(x)=e^x \)
   28 by one of the following actions:
   29 $BR
   30 (a) reflecting the graph of \(g(x)\) in the \(x\)-axis;
   31 $BR
   32 (b) reflecting the graph of \(g(x)\) in the \(y\)-axis;
   33 $BR
   34 your answer is (input a or b) \{ans_rule(15) \}
   35 $BR
   36 then, by one of the following actions:
   37 $BR
   38 (a) shifting the resulting graph to the right $a units;
   39 $BR
   40 (b) shifting the resulting graph to the left $a units;
   41 $BR
   42 (c) shifting the resulting graph upward $a units;
   43 $BR
   44 (d) shifting the resulting graph downward $a units;
   45 $BR
   46 Your answer is (input a, b, c, or d) \{ans_rule(15) \}
   47 $BR
   48 Is the domain of the function \(f(x)\) still \( (-\infty,\infty) \)?
   49 $BR
   50 Your answer is (input Yes or No) \{ans_rule(15) \}
   51 $BR
   52 The range  of the function \(f(x)\) is \( (A,\infty) \),
   53 $BR
   54 the value of \(A\) is \{ans_rule(15) \}
   55 $BR
   56 END_TEXT
   57 
   58 $ans0 = "b";
   59 $ans1 = "d";
   60 $ans2 = "Yes";
   61 $ans3 = -$a;
   62 
   63 ANS(str_cmp($ans0));
   64 ANS(str_cmp($ans1));
   65 ANS(str_cmp($ans2));
   66 ANS(num_cmp($ans3));
   67 
   68 ENDDOCUMENT();        # This should be the last executable line in the problem.
   69