Domain and Range

Front

What is the definition of Domain in mathematics?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) for which the function is defined.

Front

What is the definition of Range in mathematics?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that result from using the function.

Front

How do you denote an open interval?

Back

An open interval is denoted by parentheses, e.g., (a, b), which means that a and b are not included in the interval.

Front

How do you denote a closed interval?

Back

A closed interval is denoted by brackets, e.g., [a, b], which means that a and b are included in the interval.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain is all real numbers except x = 0, denoted as (-∞, 0) ∪ (0, +∞).

Front

What is the range of the function f(x) = x^2?

Back

The range is all real numbers greater than or equal to 0, denoted as [0, +∞).

Front

How do you find the domain of a function?

Back

To find the domain, identify all values of x that do not cause the function to be undefined (e.g., division by zero, square roots of negative numbers).

Front

What is the domain of the function f(x) = √(x - 3)?

Back

The domain is x ≥ 3, denoted as [3, +∞).

Front

What is the range of the function f(x) = -x?

Back

The range is all real numbers, denoted as (-∞, +∞).

Front

What is the domain of the function f(x) = log(x)?

Back

The domain is x > 0, denoted as (0, +∞).