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Intervals Question Type

Students enter an interval or union of intervals using standard notation.

Basic Syntax

[interval]
answer = (1, 5);

Interval Types

Bounded Intervals

[interval]
answer = [0, 10];       // Closed: both endpoints included
answer = (0, 10);       // Open: endpoints excluded
answer = [0, 10);       // Half-open: left included, right excluded
answer = (0, 10];       // Half-open: left excluded, right included

Unbounded Intervals

[interval]
answer = [5, oo);       // From 5 to infinity
answer = (-oo, 3);      // From negative infinity to 3
answer = (-oo, oo);     // All real numbers

Union of Intervals

[interval]
answer = (0, 2) U (5, 10);
answer = (-oo, 1] U [3, oo);

Empty Set

[interval]
answer = empty;

Options

answer (required)

The correct interval in standard notation.

[interval]
answer = [2, 7);

Examples

Domain of a Function

Find the domain of `f(x) = sqrt(x - 3)`.

[interval]
answer = [3, oo);

Range from Graph

From the graph, identify the range of the function.

[interval]
answer = [0, 10];

Solution to Inequality

Solve the inequality: `2x + 3 < 11`

[interval]
answer = (-oo, 4);

Piecewise Domain Restriction

Find all values of x where `f(x) = sqrt(9 - x^2)` is defined.

[interval]
answer = [-3, 3];

Union of Intervals

Find all x where `f(x) = 1/(x^2 - 4)` is defined.

[interval]
answer = (-oo, -2) U (-2, 2) U (2, oo);

Notation Rules

Notation Meaning Example
[a, b] Closed (both included) [0, 5]
(a, b) Open (both excluded) (0, 5)
[a, b) Half-open (left included) [0, 5)
(a, b] Half-open (right included) (0, 5]
oo Infinity [5, oo)
-oo Negative infinity (-oo, 3)
U Union (0, 2) U (5, 10)
empty Empty set No solutions

Grading

The system checks: - Interval notation syntax is correct - Endpoints and bracket types match - Union operations are properly formed - Returns Correct if equivalent, Incorrect otherwise

Tips

  • Review bracket notation first: Many students confuse [ with (
  • Use graphs: Visual representation helps students understand intervals
  • Connect to inequalities: Show how x < 5 becomes (-oo, 5)
  • Practice unions: These are conceptually harder; provide multiple examples
  • Test edge cases: Include questions where endpoints are critical

Common Mistakes

  • Using [5, 3) instead of (3, 5) (backwards)
  • Forgetting negative infinity has infinity direction: (-oo, 5) not (5, oo)
  • Confusing union conditions: "x < 1 OR x > 3" is (-oo, 1) U (3, oo), NOT (1, 3)

See Also