Answer Key Objects

The answer key objects (for example, 3.2; (6.45, 6.75]) specify the correct answer for the question.

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The Number Line mode uses an intuitive syntax to distinguish between objects on the number line. Note that punctuation endpoints refers to the parentheses and bracket graphing symbols.

To Do This:	Use This Notation:	Example	Notes
Single closed circle	Expressed as an evaluated number.	`3.2`
Single open circle	Expressed as an evaluated number wrapped in parentheses.	`(1.4)`
Punctuation endpoints for intervals	Expressed as evaluated numbers with the punctuation mark at the appropriate position.	`[-1.3, 2.4)`	Intervals are expressed per usual mathematical notation (i.e., the lower and upper bounds are separated by a comma).
Multiple objects and intervals	Separated by semicolons.	`3.2; (6.45, 6.75]`
Specify `-infinity` and `infinity` as left and right endpoints of intervals, respectively.		`(-infinity, 3] (5, infinity]`
Specify the answer key as no solution		`no solution`
Specify the answer key as the entire real number line		`(-infinity, infinity)`

Below are examples of malformed answer keys and the corrected version.

Malformed Example	Why?	Corrected Example
`(3,5];[4,6)`	The intervals overlap.	`(3,6)` or `(3,4;4,5;5,6)`
`3;[2,4]`	3 is in the interval [2,4].	`[2,4]` or `[2,3;3,4]`

Malformed Example

Why?

Corrected Example

(3,5];[4,6)

The intervals overlap.

(3,6)

or

(3,4;4,5;5,6)

3;[2,4]

3 is in the interval [2,4].

[2,4]

or

[2,3;3,4]

Syntax examples Since all values must be evaluated to work, no values should include expressions involving operators that are not evaluated. You must use the <eqn> tag to evaluate expressions. The following examples show the proper syntax for the answer field for both single objects and intervals. In the examples, n is an evaluated number. Type Syntax Description Single point n Closed point at x = n Single point (n) Open point at x = n Interval n0, n1 Interval between two closed points Interval (n0), (n1) Interval between two open points Interval n0, n1) Interval between a closed point at x = n0 and a right parenthesis at x = n1 Interval (n0, n1 Interval between a left parenthesis at x = n0 and a closed point at x = n1 Interval [n0, n1] Interval between a left bracket at x = n0 and a right bracket at x = n1 Interval (-infinity, n Interval between the left infinity arrow and a closed point at x = n Interval n, infinity) Interval between a closed point and the right infinity arrow Interval (-infinity, infinity) Entire real line