Domain and Range in Interval Notation

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

What does interval notation represent?

Back

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

Front

How is an open interval represented in interval notation?

Back

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

Front

How is a closed interval represented in interval notation?

Back

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

Front

What does a half-open interval mean?

Back

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

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.

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

How do you find the domain of a rational function?

Back

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

Front

What is the domain of the function f(x) = 1/(x - 3)?

Back

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