Domain and Range

Front

What is the definition of 'domain' in mathematics?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the definition of 'range' in mathematics?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Identify the domain of the function f(x) = x^2 for x in the real numbers.

Back

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

Front

Identify the range of the function f(x) = x^2 for x in the real numbers.

Back

The range is all non-negative real numbers, denoted as [0, ∞).

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) U (0, ∞).

Front

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

Back

The range is all real numbers except y = 0, denoted as (-∞, 0) U (0, ∞).

Front

How do you find the domain of a function given its equation?

Back

To find the domain, identify values that make the function undefined (like division by zero) and exclude them from the set of all real numbers.

Front

How do you find the range of a function given its equation?

Back

To find the range, determine the output values by analyzing the function's behavior and identifying any restrictions on y.

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-3)?

Back

The range is y ≥ 0, denoted as [0, ∞).