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Rewrite using MathObjects and PGML #1178

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merged 5 commits into from
Dec 18, 2024
Merged

Rewrite using MathObjects and PGML #1178

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621db75
Rewrite using MathObjects and PGML
lahvak Sep 7, 2024
750254d
Change a to the as suggested by @dlglin
lahvak Sep 20, 2024
1765ca6
Change wording as suggested by @dlglin
lahvak Sep 20, 2024
a5685a3
Use the Interval context for domain
lahvak Sep 21, 2024
86ac60e
Fix solution after switching to Interval context
lahvak Sep 21, 2024
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48 changes: 26 additions & 22 deletions OpenProblemLibrary/ma117DB/set5/srw2_9_63.pg
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Original file line number Diff line number Diff line change
Expand Up @@ -20,35 +20,39 @@ DOCUMENT(); # This should be the first executable line in the problem.

loadMacros(
"PGstandard.pl",
"PGchoicemacros.pl",
"PGML.pl",
"MathObjects.pl",
"PGcourse.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

Context("Numeric");

$a = random(2,9,1);
$ans3 = Formula("sqrt(x)-$a");

Context("Interval");

$ansInt = Compute("[-$a, infinity)");

BEGIN_PGML
The function [`f(x)=(x+[$a])^2`] is not one-to-one. Choose the largest possible
domain containing the number 100 so that the function restricted to the domain is one-to-one.

The largest possible domain is [_________________]{$ansInt} (use interval notation).
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line 43: replace "interval notation" with [@ helpLink("interval","interval notation") @]*
(including the star at the end!) This will create a link that points to instructions for entering intervals into webwork.


If [`f`] is restricted to the above domain, then the inverse function is [`g(x)=`][_______________]{$ans3}.
END_PGML

BEGIN_PGML_SOLUTION
The function [`f(x)=(x+[$a])^2`] is one-to-one on the intervals [`(-\infty, -[$a]]`] and [`[-[$a], \infty)`].
The second one contains the number 100.

TEXT(EV2(<<EOT));
The function \(f(x)=(x+$a)^2\) is not one-to-one. Choose a largest possible
domain containing the number 100 so that
the function restricted to the domain is one-to-one.
$BR
The largest possible domain is [\{ ans_rule(10) \},\{ ans_rule(10) \});
$BR
the inverse function is \(g(x)=\) \{ ans_rule(15) \}
$BR
$BBOLD
If your answer is \(\infty\), enter infinity.
$EBOLD
EOT

$ans1 = -$a;
$ans2 = "infinity";
$ans3 = "sqrt(x)-$a";
ANS(num_cmp($ans1));
ANS(str_cmp($ans2));
ANS(fun_cmp($ans3));
Solving the equation [`y=(x+[$a])^2`] for [`x`] will give us two solutions: [`x = \pm\sqrt{y} - [$a]`].
According to our domain choice, [`x \ge [$ans1]`], which means we have to choose the solution with [`+`].
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line 53: replace $ans1 with $a

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Exchanging the [`x`] and [`y`] variables will give us the answer [`g(x) = [$ans3]`].
END_PGML_SOLUTION

ENDDOCUMENT(); # This should be the last executable line in the problem.