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 \((-\infty, a]\) represent?

Back

It represents all real numbers less than or equal to 'a'. The parenthesis indicates that 'a' is included in the interval.

Front

Convert the interval notation \((a, b]\) to inequality notation.

Back

The inequality notation is \(a < x \leq b\).

Front

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

Back

It represents all real numbers 'x' such that 'x' is greater than or equal to 'a' and less than 'b'.

Front

How do you represent the solution \(x > 5\) in interval notation?

Back

The interval notation is \((5, \infty)\).

Front

What does the notation \([-3, 2)\) indicate about the endpoints?

Back

The number -3 is included in the interval (closed), while 2 is not included (open).

Front

Convert the inequality \(x \leq 10\) to interval notation.

Back

The interval notation is \((-\infty, 10]\).

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (e.g., \((a, b)\)), while closed intervals do include their endpoints (e.g., \([a, b]\)).

Front

How do you represent the solution \(z < 20\) in interval notation?

Back

The interval notation is \((-\infty, 20)\).

Front

What does the notation \((a, b)\) signify?

Back

It signifies all real numbers 'x' such that 'a < x < b', meaning 'a' and 'b' are not included.