View of /trunk/NationalProblemLibrary/Rochester/setAlgebra28ExpFunctions/srw4_1_31.pg

    1 ## DESCRIPTION
    2 ## Algebra: Exponential and Logarithmic Functions
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('exponential')
    6 ## Tagged by cmd6a 4/4/06
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Exponential and Logarithmic Functions')
   10 ## DBsection('Exponential Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 0;
   32 install_problem_grader(~~&std_problem_grader);
   33 
   34 $a=random(3,9,1);
   35 $b=random(3,9,1);
   36 
   37 BEGIN_TEXT
   38 The graph of the function
   39 \( f(x)=$b^{x-$a} \)
   40 can be obtained from the graph of
   41 \( g(x)=$b^x \)
   42 by one of the following actions:
   43 $BR
   44 (a) shifting the graph of \(g(x)\) to the right $a units;
   45 $BR
   46 (b) shifting the graph of \(g(x)\) to the left $a units;
   47 $BR
   48 (c) shifting the graph of \(g(x)\) upward $a units;
   49 $BR
   50 (d) shifting the graph of \(g(x)\) downward $a units;
   51 $BR
   52 (e) reflecting the graph of \(g(x)\) in the \(x\)-axis;
   53 $BR
   54 (f) reflecting the graph of \(g(x)\) in the \(y\)-axis;
   55 $BR
   56 Your answer is (input a, b, c, d, e, or f) \{ans_rule(15) \}
   57 $BR
   58 Is the domain of the function \(f(x)\) still \( (-\infty,\infty) \)?
   59 $BR
   60 Your answer is (input Yes or No) \{ans_rule(15) \}
   61 $BR
   62 The range  of the function \(f(x)\) is \( (A, \infty) \),
   63 $BR
   64 the value of \(A\) is \{ans_rule(15) \}
   65 $BR
   66 END_TEXT
   67 
   68 $ans1 = "a";
   69 $ans2 = "Yes";
   70 $ans3 = 0;
   71 
   72 ANS(str_cmp($ans1));
   73 ANS(str_cmp($ans2));
   74 ANS(num_cmp($ans3));
   75 
   76 ENDDOCUMENT();        # This should be the last executable line in the problem.