Interval Notation Calculator – Guide & Formulas
Convert interval notation to inequalities and graph on a number line. Enter intervals like (2, 5] or (-∞, 3) and see the inequality representation and visual display.
Convert interval notation to inequalities and graph them instantly with our free calculator. Enter any interval and see the inequality representation and number line visualization.
Key Takeaway
Use the free Interval Notation Calculator to convert interval notation to inequalities and graph on a number line. enter intervals like (2, 5] or (-∞, 3) and see the inequality representation and visual display. Get instant results with step-by-step explanations.
How to Use the Interval Notation Calculator
- Enter interval notation using ( ) for open and [ ] for closed endpoints.
- Separate multiple intervals with a union symbol (∪) or comma.
- Review the equivalent inequality representation.
- Check the number line graph with proper open/closed circle markers.
The Formula
Variable Definitions
- (a, b): Open interval: all x where a < x < b
- [a, b]: Closed interval: all x where a ≤ x ≤ b
- [a, b): Half-open: a ≤ x < b
- (a, b]: Half-open: a < x ≤ b
- ∪: Union: combines intervals (use "or" in inequality form)
Converting (-3, 7] to Inequality Notation
Convert interval notation to inequality and graph.
- Step 1: Identify the left endpoint: -3 has parenthesis ( → x > -3 (strict).
- Step 2: Identify the right endpoint: 7 has bracket ] → x ≤ 7 (inclusive).
- Step 3: Combine: -3 < x ≤ 7.
- Step 4: Graph: open circle at -3, closed circle at 7, shaded between.
Frequently Asked Questions
What does (a, b) mean in interval notation?
(a, b) is an open interval containing all real numbers strictly between a and b, not including the endpoints. It is equivalent to a < x < b.
What does [a, b] mean?
[a, b] is a closed interval containing all real numbers between a and b, including both endpoints. It is equivalent to a ≤ x ≤ b.
What is the difference between ( and [ ?
( means the endpoint is excluded (open), while [ means the endpoint is included (closed). On a number line, open = hollow circle, closed = filled circle.
How do I enter infinity?
Use "inf" or "∞" for infinity and "-inf" or "-∞" for negative infinity. Always pair infinity with a parenthesis: (5, ∞) or (-∞, 2).
What if I have two separate intervals?
Enter them separated by "U" or "union". For example, (-∞, -2) U (3, ∞) represents x < -2 or x > 3.
What is a half-open interval?
A half-open interval like [2, 5) includes one endpoint but not the other. It is equivalent to 2 ≤ x < 5.
Can I enter just a single number?
Yes. [3, 3] represents the single value x = 3. This is a degenerate interval.
How do I graph interval notation?
Plot the endpoints on a number line. Use an open circle for parentheses ( ) and a filled circle for brackets [ ]. Shade the region between the endpoints.