# DomainRange1

## Domain and Range of a Function

This PG code shows how to evaluate answers that are inequalities which use different variables.

PG problem file Explanation

Problem tagging:

```DOCUMENT();

"PGstandard.pl",
"MathObjects.pl",
"contextInequalities.pl",
);

TEXT(beginproblem());
```

Initialization: We must load `contextInequalities.pl`.

```Context("Numeric");

\$f = Compute("sqrt(x-4)");

Context("Inequalities-Only")->variables->are(x=>"Real");

\$domain = Compute("x >= 4");
```

Setup 1: We specify the context in a way that requires students to enter their answer using inequalities and the variable x. If we had used `Context("Inequalities")` instead, then students would also be able to enter answers using interval notation. For more details, please see contextInequalities.pl

We use `formatStudentAnswer=>'parsed'` and `Compute()` so that the student's answer are left as fractions rather than reduced to decimals.

```Context()->texStrings;
BEGIN_TEXT
Suppose \( f(x) = \$f \).  Enter inequalities for the
domain and range of \( f \).
\$BR
\$BR
Domain:
\{ ans_rule(20) \}
\$BR
END_TEXT
Context()->normalStrings;
```

Main Text 1:

```\$showPartialCorrectAnswers = 1;

ANS( \$domain->cmp() );
```

```Context("Inequalities-Only")->variables->are(y=>"Real");

\$range  = Compute("y >= 0");
```

Setup 2: We must reset the context and the variable so that students must enter the variable y in their answer.

```Context()->texStrings;
BEGIN_TEXT
Range:\$SPACE\$SPACE
\{ ans_rule(20) \}
END_TEXT
Context()->normalStrings;
```

Main Text 2:

```ANS( \$range ->cmp() );
```

```Context()->texStrings;
BEGIN_SOLUTION
\${PAR}SOLUTION:\${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();
```

Solution: