Problem5

Prep Main Page > Web Conference 2 > Sample Problems > Problem 5

This is Library/LoyolaChicago/Precalc/Chap8Sec3/Q38.pg

# DESCRIPTION
# Problem from Functions Modeling Change, Connally et al., 3rd ed.
# ENDDESCRIPTION

DOCUMENT();       

loadMacros("PG.pl",
           "PGbasicmacros.pl",
           "PGchoicemacros.pl",
           "PGanswermacros.pl",
           "PGgraphmacros.pl",
           "PGauxiliaryFunctions.pl",
           "extraAnswerEvaluators.pl"
           );
       
TEXT(beginproblem()); # standard preamble to each problem.

$showPartialCorrectAnswers = 0;

for ($j = 0; $j <= 1; $j++){ $mc[$j] = new_multiple_choice() };

$mc[0]->qa("If \( f(x)\cdot g(x) \) is an odd function, then both " .
           "\( f(x) \) and \( g(x) \) must be odd functions.  Be " .
           "sure you can explain your answer.","False"); 

$mc[1]->qa("If \( f(x)\cdot g(x) \) is an even function, then both " .
           "\( f(x) \) and \( g(x)  \) must be even functions.  Be " .
           "sure you can explain your answer.","False"); 

for ($k = 0; $k <= 1; $k++){ $mc[$k]->extra("True");
                             $mc[$k]->makeLast("False") };

@explain = ("The statement is false.  For example, if \( f(x)=x \) " .
            "and \( g(x)=x^2 \), then \( f(x) \cdot g(x)=x^{3} \). " .
            "In this case, \( f(x) \cdot g(x) \) is an odd function, " .
            "but \( g(x) \) is an even function.",
            "The statement is false.  For example, if \( f(x)=x \) " .
            "and \( g(x)=x^3 \), then \( f(x) \cdot g(x)=x^{4} \). " .
            "In this case, \( f(x) \cdot g(x) \) is an even function, " .
            "but both \( g(x) \) and \( f(x) \) are odd functions.");

$i = random(0,1,1);

BEGIN_TEXT
Question 38:
$BR
$SPACE
$BR
Is the following statement true or false?
$BR $SPACE $BR
\{ $mc[$i]->print_q() \}
$BR
\{ $mc[$i]->print_a() \}

END_TEXT

ANS(radio_cmp($mc[$i]->correct_ans));

SOLUTION(EV3(<<'END_SOLUTION'));
$BR $SPACE $BR 
$BBOLD  SOLUTION $EBOLD
$BR 
$explain[$i]
END_SOLUTION

ENDDOCUMENT();