Interval Notation

Front

What is interval notation?

Back

Interval notation is a mathematical notation used to represent a range of values on the number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the interval notation (a, b) represent?

Back

The interval notation (a, b) represents all real numbers x such that a < x < b. The endpoints a and b are not included.

Front

What does the interval notation [a, b] represent?

Back

The interval notation [a, b] represents all real numbers x such that a ≤ x ≤ b. The endpoints a and b are included.

Front

What does the interval notation (a, b] represent?

Back

The interval notation (a, b] represents all real numbers x such that a < x ≤ b. The endpoint a is not included, while b is included.

Front

What does the interval notation [a, b) represent?

Back

The interval notation [a, b) represents all real numbers x such that a ≤ x < b. The endpoint a is included, while b is not included.

Front

How is infinity represented in interval notation?

Back

Infinity is represented by the symbol ∞. In interval notation, it is always used with parentheses, e.g., (a, ∞) or (-∞, b).

Front

Can you use the symbols [ or ] with infinity?

Back

No, you cannot use the symbols [ or ] with infinity in interval notation.

Front

What does the interval notation (-∞, b) represent?

Back

The interval notation (-∞, b) represents all real numbers x such that x < b. The endpoint b is not included.

Front

What does the interval notation [a, ∞) represent?

Back

The interval notation [a, ∞) represents all real numbers x such that x ≥ a. The endpoint a is included.

Front

How do you graph the inequality x < 5 on a number line?

Back

To graph x < 5, draw a number line, place an open dot at 5, and shade to the left to indicate all numbers less than 5.