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

What does the notation [a, b] represent in interval notation?

Back

It represents a closed interval, including the endpoints a and b.

Front

What does the notation (a, b) represent in interval notation?

Back

It represents an open interval, excluding the endpoints a and b.

Front

What does the notation [a, b) represent in interval notation?

Back

It represents a half-open interval, including the endpoint a but excluding the endpoint b.

Front

What does the notation (a, b] represent in interval notation?

Back

It represents a half-open interval, excluding the endpoint a but including the endpoint b.

Front

What is the range of the function f(x) = x^2 for all real numbers x?

Back

The range is [0, ∞) because the output (y) is always non-negative.

Front

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

Back

The domain is all real numbers except x = 0, which can be written as (-∞, 0) ∪ (0, ∞).

Front

How do you find the range of a linear function?

Back

For a linear function of the form f(x) = mx + b, the range is all real numbers, or (-∞, ∞), unless restricted by the context.

Front

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

Back

The domain is [1, ∞) because the expression under the square root must be non-negative.