# 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();

"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGgraphmacros.pl",
"PGauxiliaryFunctions.pl",
);

TEXT(beginproblem()); # standard preamble to each problem.

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

$mc->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->qa("If $$f(x)\cdot g(x)$$ is an even function, then both " .
"$$f(x)$$ and $$g(x)$$ must be even functions.  Be " .

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();