## DESCRIPTION
## Introduction to WeBWorK
## ENDDESCRIPTION

## KEYWORDS('functions', 'enter numerical answers')
## Tagged by XW

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('WeBWorK Tutorial')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

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

$a = random(-10,-1,1);
$b = random(1,11,1);
$c = random(1,11,1);
$d = random(1,11,1);

BEGIN_TEXT
This problem set demonstrates how you enter numerical answers into WeBWorK. 

$PAR

In these problems you need to enter a number, since we're checking whether you can does these calculations. Do the calculation, then enter the correct numerical result in the box provided. 

$PAR

$BBOLD Warning: $EBOLD While you might use a calculator here, you may not be allowed a calculator on some of your tests.

$PAR

END_TEXT

BEGIN_TEXT
$HR
$PAR
Evaluate the expression \(0($a)(-2($d ))\):   \{ ans_rule(5) \}

$PAR

END_TEXT

$ans = 0*($a)*(-2*($d))  ;
ANS(num_cmp($ans, mode=>"strict"))     ;

BEGIN_TEXT
$HR
$PAR

Evaluate the expression \(  $a ($b )($c + $d)  \):   \{ ans_rule(10) \}

$PAR

END_TEXT

$ans = $a * $b *($c + $d)      ;
ANS(num_cmp($ans, mode=>"strict"))     ;

BEGIN_TEXT
$HR
$PAR

Evaluate the expression \(  ($a + $b )($c + 12 ($d))  \):   \{ ans_rule(5) \}

$PAR

END_TEXT

$ans = ($a + $b )*($c + 12 * $d) ;
ANS(num_cmp($ans, mode=>"strict"))       ;

BEGIN_TEXT

$PAR
$HR
$PAR

For some problems, you will be able to get WeBWorK to do some of the work for you.  

$PAR

For example, calculate ($a) * ($b): \{ ans_rule()\}

$PAR

END_TEXT

$ans = $a*$b;

ANS(num_cmp($ans));

BEGIN_TEXT

$PAR

The asterisk is how most calculators and computers show multiplication and you can use this with WeBWorK. But WeBWorK will also allow you to use a space to show multiplication. You can either \($a * $b\) or \{$a*$b\}.  All will work. Try them.

$PAR
$HR
$PAR

Now try calculating  $SPACE \( \sqrt{7}\)$SPACE,  the square root of 7.

$PAR

You can enter this as sqrt(7), or as 7$CARET(1/2).  This is because
WeBWorK knows about standard calculations like square root, and that roots can
be represented using fractional exponents. You'll study this in detail very shortly.  

$PAR

Note, exponents can be entered with either
a $CARET (caret) or ** (two asterisks).
Try it in the box below.

$PAR

\( \sqrt{7} = \) \{ ans_rule(20) \}

$PAR
$HR
$PAR

END_TEXT

ANS(num_cmp("sqrt(7)") );

BEGIN_TEXT

When it is very clear that only multiplication is involved, you can simpley write two characters together

$PAR

E.g., enter the square root of 5 divided 3.
You can enter this as 2*sqrt(5/3) or more simply as 2sqrt(5/3).  Try it:

$PAR

\( 2\sqrt{5/3} =  \) \{ ans_rule(20) \}

$PAR

END_TEXT

ANS(num_cmp("2*sqrt(5/3)") );

BEGIN_TEXT

$PAR
$HR
$PAR

Think about the problem above. How sure are you that we should divide 5 by 3 then take the square root. If we are verablizing the process, we could say "divide 5 by 3 then take the square root of the result." It is a little longer to say, but very clear. In written math (symbology) sometimes you need to use ( )'s to make your meaning clear. 

$PAR

E.g. 1/2+3 is 3.5, but  1/(2+3) is .2 Why?
Try entering both and use the ${LQ}Preview${RQ} button below to see the difference.  In addition to ( )'s, you can also use [ ]'s and \(\lbrace \rbrace\).  

$PAR

\( (1/2) + 3 = \)\{ ans_rule(20) \}

$PAR

Now go back to the previous problem and enter 2sqrt5/3 instead of 2sqrt(5/3).  Use the ${LQ}Preview${RQ} button to see how WeBWorK interprets the symbology. 

END_TEXT

ANS(num_cmp(3.5));

BEGIN_TEXT
$PAR
$HR
$PAR

When entering numbers, leave off units (or dollar signs for money) unless the
problem directs you to do otherwise.

$PAR

For example, if we want to know how much money you will have if you collect $DOLLAR 100 from 200 people, the answer is $DOLLAR 20,000.

$PAR

When entering this value, you should just give 20000 (or 100*200). 

$PAR

When doing WeBWorK problems alsways look "outside the (answer) box." If the problems has units associated, they are usually provided. Don't include the stuff already provided outside the box!

$PAR

$DOLLAR 100 from 200 people yields $DOLLAR \{ ans_rule(20) \}

$PAR
$HR
$PAR

You can always try to enter answers and let WeBWorK do the calculating. After a little experience, you may find that the WeBWorK preview lets you "see" the answer you would type into your calculator in the same form as a textbook or a correctly expression. It is a great way to find mistakes like omitted parentheses or incorrect grouping.

$PAR

Or, if you have trouble with the syntax while entering expressions, you
can compute most answers on yourself then type the answer into
WeBWorK.  If you do, just be sure to include lots of decimal places
(including the first 5 non-zero places should be safe).

$PAR

$BBOLD In general, there is no penalty for getting an answer wrong.$EBOLD  If you
are limited in the number of attempts you get for a problem, you will
be warned by the problem itself (this could happen, for example, on a
true/false question).  What counts is that you get the answer right
before the due date. 

$PAR

$BBOLD However, $EBOLD even though you get a "correct" from WeBWorK, if that answer comes from an invalid mathematical process (in relation to your problem), your instructor will almost certainly catch it in written work! Be certain you understand the process and can write the steps for each problem answered in correctly.

$PAR
	
$BBOLD Remember: $EBOLD For complicated answers you should use the ${LQ}Preview${RQ} button to check for syntax errors and also to check that the answer you enter is really what you think it is.

END_TEXT

ANS(num_cmp("100*200"));

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

## DESCRIPTION
## Introduction to WeBWorK
## ENDDESCRIPTION

## KEYWORDS('functions', 'enter functions')
## Tagged by XW

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('WeBWorK Tutorial')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

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


BEGIN_TEXT
This problem demonstrates how you enter function answers into WeBWorK.

$PAR
	
First enter the absolute value of -7 in the box below.

$PAR

\{ans_rule(35) \}
$PAR

When entering the answer, you should just enter the value 7. But WeBWorK will also accept abs -7 or even abs-7.

$PAR

$BBOLD Warning:$EBOLD WeBWorK will accept this or any other value equal to abs(-7), e.g. 7, or 14/2, or sqrt(49). However your instructor is almost certain to notice one of those incorrect ways of getting to a correct answer on a written assignment!

END_TEXT

$ans = "abs(-7)";
ANS(fun_cmp($ans, limits=>[[0.2, 100]]));

BEGIN_TEXT

$PAR
$HR
$PAR
	
It is better to enter abs(x), even though WeBWorK will also accept abs
x or even absx, because you are less likely to make a mistake.  Try
entering abs(2x) without the parentheses and you may be surprised at
what you get. Use the Preview button to see what you get. 

$PAR
 
WeBWorK will evaluate standard calculations (such as abs or sqrt) before doing anything else, so abs 2x means first find the absolute value of 2 which gives abs(2) and then multiply by x.

$PAR

Try it.  \{ans_rule(35) \}

END_TEXT


$ans = "abs(2*x)";
ANS(fun_cmp($ans, limits=>[[0.2, 100]]));

BEGIN_TEXT

$PAR
$HR
$PAR

Now enter the calculation \(2\sqrt{ t}\) using 2sqrt(t). 
 \{ans_rule(35) \}

$PAR

Note this uses the variable \(t\) and not \(x\). Try entering 2sqrt(x) and see what happens. Be carful to read the error statements in WeBWorK. They are trying to tell you where you made an error.

$PAR

When WeBWork says an answer doesn't \(parse\) correctly, that is it's overly computerish way of saying the answer doesn't fit the problem. It will also try to warn you that a parenthesis  or some other closing symbol is missing.

$PAR

$BBOLD Here's a tip from the lazy side! $EBOLD If you can highlight a text in a WeBWorK page, you can drag and drop it or copy into the answer box! Try it out. Enter 2sqrt(t) in the box above by highlighting, dragging and dropping. Be careful about picking up extra characters. But if you picked up an improperly placed period or comma, WeBWork will show you the error when you submit your answer. Drag/drop and copy make it much easier to do substitutions in formulas.

$PAR


END_TEXT

$ans = "2*sqrt(t)";
ANS(fun_cmp($ans,var=>'t', limits=>[[0,100]]));

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

## DESCRIPTION
## Introduction to WeBWorK
## ENDDESCRIPTION

## KEYWORDS('functions', 'order of operations')
## Tagged by XW

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('WeBWorK Tutorial')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

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


BEGIN_TEXT
	
This problem will review $BBOLD order of operations,$EBOLD i.e. rules of precedence or order in which mathematical operations are performed.

$PAR

The rules are simple.  Exponentiation is always done before multiplication 
and division, and multiplication and division are always done before addition 
and subtraction. (Mathematically we say exponentiation takes precedence over 
multiplication and division, etc.). For example what is 1+2*3? You can use parentheses (and also square brackets [ ] or curly braces \(\lbrace \rbrace\)) if you want to change the normal way operations work.

$PAR

$BBOLD Note:$EBOLD You must compute this number before entering it
	into WeBWorK.

$PAR

1+2*3 = \{ ans_rule(25) \}

$PAR

END_TEXT

$ans = 7;
ANS(num_cmp($ans, mode=>'strict'));

BEGIN_TEXT

$BBOLD Note:$EBOLD You must compute this number before entering it
	into WeBWorK.


$PAR

What is \( 2\cdot 3^2 \)?  \{ ans_rule(25) \}

END_TEXT

$ans = 2*3**2;
ANS(num_cmp($ans, mode=>'strict'));

BEGIN_TEXT

$PAR
$HR
$PAR

Now sometimes you want to force things to be done in a different way. This is
what parentheses are used for.
 
$PAR
 
$BBOLD Rule 1:$EBOLD Groups are simplified first. IE, Whatever is enclosed in parentheses (--), braces {--}, brackets [--], all in a numerator, all in a denominator, within an absolute value symbol |--|, or all under a radical \( \sqrt{x}\) are done before anything else (and things in the inner most parentheses are done first). 

$PAR

For example, simplfy the following expression yourself, then enter the expression in the box below:

$PAR

\[ \frac {1+|9-3|}{2+\sqrt{49}}\]

$PAR

$BBOLD  Hint: $EBOLD This is a good place to use [ ]'s and also to use the ${LQ}Preview${RQ} button. Also remember, |x| in standard notation is absolute value of x, so you must replace |x| with abs(x).

$PAR

\{ ans_rule(25) \}

END_TEXT

$ans = "(1+abs(9-3))/(2+sqrt(49))" ;
ANS(num_cmp($ans));

BEGIN_TEXT

$PAR
$HR
$PAR

Here are some more examples:

(1+3)9 = 36, (2*3)**2 = 6**2 = 36, 3**(2*2) = 3**4 = 81,
	(2+3)**2 = 5**2 = 25, 3**(2+2) = 3**4 = 81

$PAR

(Here we have used ** to denote exponentiation and you can also use this instead of a ${LQ}caret${RQ} if you want).  Try entering some of these and use the "Preview" button to see the result.  The "correct"
result for this answer blank is 36, but by using the ${LQ}Preview${RQ} button, you can enter whatever 
you want and use WeBWorK as a hand calculator.

$PAR

\{ ans_rule(25) \}

$PAR
$HR
$PAR

END_TEXT

$ans =36;

ANS(num_cmp($ans));

BEGIN_TEXT

$PAR

$BBOLD Rule 2:$EBOLD The correct order of evaluation is 
> Roots and Powers (Exponents)
> Division and Multiplication
> Subtractions and Additiion

Think! Correct order of operations goes from the hardest stuff (Roots) first to the easiest stuff (Addition) last.

$PAR
 
There is one other thing to be careful about.  Multiplication and
division have the same precedence.  For example, what does 2/3*4 mean?
(Note that / is the "division symbol", which is sometimes written as a
line with two dots. Don't think of / as the horizontal line in a
fraction. Ask yourself what 1/2/2 should mean.)  
 
$PAR
 
$BBOLD Rule 3:$EBOLD  Multiplication and divsion are evaluated from left to right.
 
$PAR
 
Example: 2/3*4 means (2/3)*4 = 8/3, IT DOES NOT MEAN 2/12.  If you want 2/(3*4) = 2/12, you have to use parentheses.

$PAR

$BBOLD Rule 4:$EBOLD  Addition and subtraction are evaluated from left to right.
 
$PAR
 
Example: The same thing happens with addition and subtraction as with multiplication and division. Notice 1-3+2 = 0, but 1-(3+2) = -4. 

$PAR

This aare many situations where using parentheses might be a good idea, even if they are not needed

$PAR

Example: Write (2/3)*4 rather than 2/3*4. This is also a case where previewing your answer can save you a lot a grief since you will be able to see what
you entered.

$PAR

Enter 2/3*4 and use the Preview button to see what you get.

$PAR

\{ ans_rule(25) \}

$PAR

END_TEXT

$ans = 8/3;
ANS(num_cmp($ans));

BEGIN_TEXT

$PAR
$HR
$PAR

$BBOLD A Hand-in Assignment $EBOLD

$PAR

Here's the link to the 
\{htmlLink(qq! http://webwork.asu.edu/availableFunctions.html!, "list of the functions") \}  which WeBWorK understands. WeBWorK ALWAYS uses radian mode for trig functions.

$PAR

$BBOLD 1. Click on the link. Print out this list and turn it in to your instructor before the due date of this assignment.  

$PAR

2. On the back of the list of functions, write the rules for the correct order of operations. 

$PAR

3. Also on the back of the page, calculate the following expression exactly. Show all steps as your apply order of operations.

$PAR

\[ \frac {3+|9-13|}{2+\sqrt{29-4}}\]

$PAR

4. Look up the word "function" in your textbook. Write a defintion for "function" and provide a simple example of the concept.

$EBOLD

END_TEXT

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

## DESCRIPTION
## Introduction to WeBWorK
## ENDDESCRIPTION

## KEYWORDS('functions', 'enter letters or words', 'true or false questions')
## Tagged by XW

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('WeBWorK Tutorial')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

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

BEGIN_TEXT
This part demonstrates WeBWorK problems where you enter letters
or words.  We start with a True/False question.

$PAR

Enter a $BITALIC T $EITALIC or an $BITALIC F $EITALIC in
each answer space below to indicate whether the corresponding statement is true or
false.

$PAR

END_TEXT

## First we set up our variables.
$a = random(1,5,1);
$b = random(6,10,1);
$c = random(-10,-1,1);
$d = random(-10,-1,1);
$e = random(1,10,1);
$f = random(5,10,1);

$questStr1 = EV2(" \(  -$a   \lt    -$b              \) ");
$ansStr1 = "F";
$questStr2 = EV2(" \(   $c   \leq    $c              \) ");
$ansStr2 = "T";
$questStr3 = EV2(" \(   $d   \lt     $d              \) ");
$ansStr3 = "F";
$questStr4 = EV2(" \(   \pi  \geq    \frac{22}{7}    \) ") ;
$ansStr4 = "F";
$questStr5 = EV2(" \(  \sqrt {$e+3}  \geq    \sqrt $e + \sqrt 3    \) ");
$ansStr5 = "F";
$questStr6 = EV2(" \(  \sqrt {$f-3}  \geq    \sqrt $f - \sqrt 3    \) ");
$ansStr6 = "T";
$questStr7 = EV2(" \(  \sqrt {$f*$e}  \geq    \sqrt $e \sqrt $f    \) ");
$ansStr7 = "T";

@questions =( $questStr1,$questStr2,$questStr3,$questStr4,$questStr5,$questStr6,$questStr7);
@answers =( $ansStr1,$ansStr2,$ansStr3,$ansStr4,$ansStr5,$ansStr6,$ansStr7);

## Now choose randomly 5  questions out of the 7 question strings above.

@slice = NchooseK(scalar(@questions),5);

## Next we output the 5 chosen questions. #
TEXT( &match_questions_list(@questions[@slice]) );

ANS(str_cmp([ @answers[@slice] ] ));

TEXT(<<EOT);

$PAR

Notice that if one of your answers is wrong then, in this problem,
WeBWorK will tell you which parts are wrong and which parts are right.
This is the behavior for most problems, but for true/false or multiple
choice questions WeBWorK will usually only tell you whether or not all
the answers are correct.  It won't tell you which ones are wrong.  The
idea is to encourage you to think rather than to just try guessing.

$PAR Typically all of the answers must be correct before you get
credit for a problem like this.
EOT

BEGIN_TEXT

$PAR
$HR
$PAR

Now we have a question where the answer involves a word.  When a word is
a possible answer, we will usually emphasize your options by using
$BITALIC italics $EITALIC. Where would this happen? 

$PAR

Well, we might have a situation where we have division by zero. Of course, we all know that this is $BITALIC undefined $EITALIC.

$PAR

We might also try to take the square root (or even root) of a negative number. This is also $BITALIC undefined $EITALIC if we expect to get a real number as an answer. 

$PAR
$HR
$PAR

Evaluate the following expressions.  Exact real number answers are required for each problem. When one of them does not evaluate to a real number, type $BITALIC undefined $EITALIC  in its answer box. Also, if you try to enter the calculation into WeBWorK for an $BITALIC undefined $EITALIC process, WeBWorK will NOT give you credit. 

$PAR

Pay attention to how placing parentheses, shifting the location of a negative sign, or changing an operation can change the result of the calculations.

END_TEXT

BEGIN_TEXT
$PAR

$BBOLD 6. $EBOLD $SPACE (2/3-3) = \{ ans_rule(20) \}

END_TEXT

ANS(str_cmp("-7/3"));

BEGIN_TEXT
$PAR

$BBOLD 7. $EBOLD $SPACE 2/(3-3) = \{ ans_rule(20) \}

END_TEXT

ANS(str_cmp("undefined"));

BEGIN_TEXT
$PAR

$BBOLD 8. $EBOLD $SPACE (4-4)/(3*3) = \{ ans_rule(20) \}

END_TEXT

ANS(str_cmp("0"));

BEGIN_TEXT
$PAR

$BBOLD 9. $EBOLD $SPACE (4-4)/(3-3) = \{ ans_rule(20) \}

END_TEXT

ANS(str_cmp("undefined"));

BEGIN_TEXT

$PAR

$BBOLD 10. $EBOLD $SPACE \( -\sqrt{25}\) = \{ ans_rule(20) \}

$PAR

END_TEXT

$ans = "-sqrt(25)" ;
ANS(num_cmp($ans));

BEGIN_TEXT

$PAR

$BBOLD 11. $EBOLD $SPACE \( \sqrt{-25}\) = \{ ans_rule(20) \}

$PAR

END_TEXT

ANS(str_cmp("undefined"));


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

## DESCRIPTION
## Introduction to WeBWorK
## ENDDESCRIPTION

## KEYWORDS('functions', 'sample', 'interval')
## Tagged by XW

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('WeBWorK Tutorial')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"extraAnswerEvaluators.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 0;


BEGIN_TEXT
This problem demonstrates WeBWorK questions where the answer is a list of
 numbers
or an interval.
$PAR
Enter the first three numbers of the form \( n^2 \), where \(n\) is a
positive integer, as a comma separated list.
$BR
\{ ans_rule(30) \}
$BR
You could have entered your answer as "1, 4, 9" (without the quotes), or
as "4, 1, 9", or as "2 $CARET 2, 1 $CARET 2, 3 $CARET 2".  The order of the
numbers does not matter, and you can still let WeBWorK evaluate expressions
for you.
$PAR
END_TEXT	

	ANS(number_list_cmp("1^2, 2^2, 3^2" ) );

BEGIN_TEXT
$PAR
$HR
$PAR
Now we will enter a few intervals from the real line.  WeBWorK can
handle standard interval notation.  In each case, we will describe the
	set in a couple of ways, and then show you how to enter it.  Let's start
with real numbers satisfying \(2\le x <5\).  The usual interval notation
for this is \( [2, 5) \).
$BR
Enter it just as shown:  \{ ans_rule(30) \}
$BR
Note, you can follow the usual WeBWorK conventions when entering the
numbers in the interval, so you could also enter [ log(100), 2**2 + 1).
  Try it.  Previewing your answer can help here too if you are having
WeBWorK evaluate your answer.
$PAR
With intervals, there is a difference between square brackets [] (which mean
to include the end point) and parentheses () (which mean to not include the
end point), and you will need to get them right to have the interval
correct.
END_TEXT	
ANS(interval_cmp("[2, 5)"));

BEGIN_TEXT
$PAR
$HR
$PAR
If we want to enter an interval where one side is unbounded, such as
the real numbers greater than 3, we would normally write
\( (3, \infty) \).  Since computer keyboards do not come with an
infinity symbol, we just write out the word $BITALIC infinity $EITALIC.
So, enter (3, infinity).
$BR
 \{ ans_rule(30) \}
$BR
If we had wanted \(-\infty\), we would type $BITALIC -infinity $EITALIC
instead
END_TEXT	
ANS(interval_cmp("(3, infinity)"));

BEGIN_TEXT
$PAR
$HR
$PAR
Finally, sometimes intervals come in more than one piece.  For example,
the inequality
\( x^2 \ge 25 \)
is satisfied with \( x \ge 5 \) and also when \( x \le -5\).
This would be normally written as the union of two intervals:
\[ (-\infty, -5] \cup [5, \infty) \]
To type this into WeBWorK, we just use a capital U for the union symbol:
(-infinity, -5] U [5, infinity)
$BR
 \{ ans_rule(30) \}
$BR
When using unions of intervals, the order of the smaller intervals does not
	matter, so you could also enter [5, infinity) U (-infinity, -5].
	$BR
END_TEXT
	
ANS(interval_cmp("(-infinity, -5] U [5, infinity)"));

BEGIN_TEXT
$PAR
$HR
$PAR
Be aware that if you enter intervals which overlap, such as [2, 10)
 U (7, 15), WeBWorK will expect you to simplify it into a single interval,
	in this case [2, 15).
	$BR
	 \{ ans_rule(30) \}
$BR
END_TEXT

ANS(interval_cmp("[2, 15)"));

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

## DESCRIPTION
## Introduction to WeBWorK
## ENDDESCRIPTION

## KEYWORDS('functions', 'enter functions')
## Tagged by XW

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('WeBWorK Tutorial')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

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


BEGIN_TEXT
<B>WeBWorK can accept a number, mathematical expression or even a complete sentence. In this example you are asked to enter a mathematical expression. It wants you to type in (x+2)^2. You will study this problem in a later lesson.</B>
<BR>
<BR>
Consider a function f(x)=x^2. This is the squaring rule. It says "take a number and square it."
<BR>
<BR>
If the graph of a new function g(x)is the graph of f(x) shifted to the left 2 units, what is the algebraic expression for the function g(x)?
<BR>
<BR>
g(x) = 
\{ans_rule(20) \}

END_TEXT

ANS(fun_cmp("(x+2)^2"));

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