Domain and Range in Interval Notation

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

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

Interval notation is a way of writing subsets of the real number line using intervals, indicating the start and end points.

An open interval (a, b) means that the endpoints a and b are not included in the interval.

A closed interval [a, b] means that the endpoints a and b are included in the interval.

A half-open interval [a, b) includes the endpoint a but not b, while (a, b] includes b but not a.

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

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

The domain is all real numbers except where the denominator is zero.

The domain is (-∞, 3) ∪ (3, ∞) because x cannot equal 3.