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 notation \( (a, b) \) represent?

Back

The notation \( (a, b) \) represents an open interval, meaning that the endpoints \( a \) and \( b \) are not included in the interval.

Front

What does the notation \( [a, b] \) represent?

Back

The notation \( [a, b] \) represents a closed interval, meaning that the endpoints \( a \) and \( b \) are included in the interval.

Front

What does the notation \( (-\infty, a) \) represent?

Back

The notation \( (-\infty, a) \) represents all real numbers less than \( a \), with \( a \) not included.

Front

What does the notation \( [a, \infty) \) represent?

Back

The notation \( [a, \infty) \) represents all real numbers greater than or equal to \( a \), with \( a \) included.

Front

When graphing inequalities, what does a closed dot indicate?

Back

A closed dot indicates that the endpoint is included in the solution set, used for symbols \( \leq \) and \( \geq \).

Front

When graphing inequalities, what does an open dot indicate?

Back

An open dot indicates that the endpoint is not included in the solution set, used for symbols \( < \) and \( > \).

Front

Convert the interval notation \( (-\infty, 0] \) to inequality notation.

Back

The inequality notation is \( x \leq 0 \).

Front

Convert the interval notation \( [3, 7) \) to inequality notation.

Back

The inequality notation is \( 3 \leq x < 7 \).

Front

Can you use the symbols [ or ] with infinity?

Back

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