View of /branches/Rogawski_Calculus/2e/1_Precalculus_Review/1.1_Real_Numbers_Functions,_Equations_and_Graphs/1.1.71

    1 ## DBsubject('Algebra')
    2 ## DBchapter('Functions')
    3 ## DBsection('Domain and Range')
    4 ## KEYWORDS('calculus', 'intervals','domain', 'range', 'functions')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('2')
    7 ## AuthorText1('Rogawski')
    8 ## Section1('1.1')
    9 ## Problem1('71')
   10 ## Author('Carol Panepinto')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 
   18 $x = random(3,10);
   19 $y = random(11,20);
   20 $z = random(1,8);
   21 $k = random(9,18);
   22 
   23 $a = Interval("[$x,$y]");
   24 $b = Interval("[($z),($k)]");
   25 
   26 $n = random(2,5);
   27 
   28 $ansad = Interval("[($x),($y)]");
   29 $ansar = Interval("[($z+$n),($k+$n)]");
   30 $solarx = Formula($z+$n);
   31 $solary = Formula($k+$n);
   32 
   33 $ansbd = Interval("[$x-$n,$y-$n]");
   34 $ansbr = Interval("[$z,$k]");
   35 $solbdx = Formula($x-$n);
   36 $solbdy = Formula($y-$n);
   37 
   38 $anscd = Interval("[$x/$n,$y/$n]");
   39 $anscr = Interval("[$z,$k]");
   40 
   41 $ansdd = Interval("[$x,$y]");
   42 $ansdr = Interval("[$n*$z,$n*$k]");
   43 $soldd = Formula($n*$z);
   44 $soldr = Formula($n*$k);
   45 
   46 Context()->texStrings;
   47 BEGIN_TEXT
   48 \{ beginproblem() \}
   49 \{ textbook_ref_exact("Rogawski ET 2e", "1.1","71") \}
   50 $PAR
   51 Suppose that \(f(x)\) has a domain of \($a\) and a range of \($b\).  What are the domain and range of:$PAR
   52 (a) $BBOLD \(f(x) + $n\) $SPACE
   53  Domain $EBOLD \{ans_rule(10)\} $SPACE
   54 $BBOLD Range $EBOLD \{ans_rule(10)\}  $PAR
   55 
   56 (b) \(f(x+$n)\) $SPACE
   57 $BBOLD Domain \{ans_rule(10)\} $SPACE
   58 Range $EBOLD \{ans_rule(10)\}  $PAR
   59 
   60 
   61 (c) \(f($n x)\) $SPACE $SPACE $SPACE $SPACE
   62 $BBOLD Domain \{ans_rule(10)\}  $SPACE
   63 Range $EBOLD \{ans_rule(10)\}  $PAR
   64 
   65 (d) \($n f(x)\) $SPACE $SPACE $SPACE $SPACE
   66 $BBOLD Domain \{ans_rule(10)\}  $SPACE
   67 Range $EBOLD \{ans_rule(10)\}  $PAR
   68 
   69 
   70 $PAR
   71 
   72 END_TEXT
   73 Context()->normalStrings;
   74 
   75 ANS($ansad->cmp);
   76 ANS($ansar->cmp);
   77 ANS($ansbd->cmp);
   78 ANS($ansbr->cmp);
   79 ANS($anscd->cmp);
   80 ANS($anscr->cmp);
   81 ANS($ansdd->cmp);
   82 ANS($ansdr->cmp);
   83 
   84 Context()->texStrings;
   85 SOLUTION(EV3(<<'END_SOLUTION'));
   86 $PAR
   87 $SOL
   88 $PAR
   89 (a) \(f(x)+$n\) is obtained by shifting \(f(x)\) upwards by \($n\) units.  Therefore the domain remains \([$x,$y]\) while the range becomes \([$solarx, $solary]\).
   90 $PAR
   91 (b) \(f(x+$n)\) is obtained by shifting \(f(x)\) by \($n\) units left along the x axis.  Therefore the domain becomes \([$solbdx, $solbdy]\) while the range remains \([$z, $k]\).
   92 $PAR
   93 (c) \(f($n x)\) is obtained by compressing \(f(x)\) by a factor of \($n\).  Therefore the domain becomes \([\frac{$x}{$n},\frac{$y}{$n}]\) while the range remains \([$z,$k]\).
   94 $PAR
   95 (d) \($n f(x)\) is obtained by stretching \(f(x)\) vertically by a factor of \($n\).  Therefore the domain remains \([$x,$y]\) while the range becomes \([$soldd, $soldr]\).
   96 $PAR
   97 END_SOLUTION
   98 
   99 ENDDOCUMENT();