Domain and Range in Interval Notation

Front

What is the definition of 'Domain' in interval notation?

Back

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

Front

What is the definition of 'Range' in interval notation?

Back

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

Front

What does the interval notation [-4, 5] represent?

Back

It represents all real numbers x such that -4 ≤ x ≤ 5, including the endpoints -4 and 5.

Front

What does the interval notation (3, ∞) represent?

Back

It represents all real numbers x such that x > 3, not including the endpoint 3.

Front

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

Back

The domain is [3, ∞) because the expression under the square root must be non-negative.

Front

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

Back

The range is [0, ∞) because the output of x^2 is always non-negative.

Front

What does the interval notation (-∞, 1] represent?

Back

It represents all real numbers x such that x ≤ 1, including the endpoint 1.

Front

What is the domain of the function f(x) = 1/(x - 4)?

Back

The domain is (-∞, 4) ∪ (4, ∞) because x cannot equal 4 (the denominator cannot be zero).

Front

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

Back

The range is (-∞, 0) ∪ (0, ∞) because the function never outputs zero.

Front

What does the interval notation [-3, ∞) represent?

Back

It represents all real numbers x such that x ≥ -3, including the endpoint -3.