Interval Notation, domain and range

Front

What is interval notation?

Back

A mathematical notation used to represent a range of values, typically expressed using parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the notation (a, b) represent?

Back

An open interval where 'a' and 'b' are not included in the range.

Front

What does the notation [a, b] represent?

Back

A closed interval where 'a' and 'b' are included in the range.

Front

What does the notation [a, b) represent?

Back

A half-open interval where 'a' is included and 'b' is not included.

Front

What does the notation (a, b] represent?

Back

A half-open interval where 'a' is not included and 'b' is included.

Front

How do you find the domain of a function from its graph?

Back

By identifying the x-values for which the function is defined, typically reading from left to right.

Front

How do you find the range of a function from its graph?

Back

By identifying the y-values that the function can take, typically reading from bottom to top.

Front

What is the domain of the function f(x) = √(x - 4)?

Back

[4, ∞) because the expression under the square root must be non-negative.

Front

Express the inequality x > 5 in interval notation.

Back

(5, ∞) because 5 is not included in the range.

Front

Express the inequality -3 ≤ x < 2 in interval notation.

Back

[-3, 2) because -3 is included and 2 is not.