Answer Key Objects

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

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) 

Note:
  • Two answer key objects must not be placed so that they are less than 1/4 of the distance between two consecutive tickmarks.
  • If an answer key object is overlapping a tickmark but the answer is not actually on the tickmark, your tickmark spacing is too small. Decrease the range attribute to a smaller range.

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]
Note: If for some reason your answer key cannot be understood — because of a typographical or other error — by default the key changes to -2;[1,3] with a default range of -5 to 5. If you see this answer key unexpectedly, there is a problem with the answer key you specified.

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