Domain and Range of Functions with Interval Notation

Front

What is the domain of a function?

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 range of a function?

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

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

Back

The notation (a, b) means that the interval includes all numbers between a and b, but not a and b themselves (open interval).

Front

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

Back

The notation [a, b] means that the interval includes all numbers between a and b, including a and b themselves (closed interval).

Front

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

Back

The notation (a, b] means that the interval includes all numbers between a and b, including b but not a (half-open interval).

Front

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

Back

The notation [a, b) means that the interval includes all numbers between a and b, including a but not b (half-open interval).

Front

How do you express the domain of a function that is defined for all real numbers?

Back

The domain can be expressed as (-∞, ∞) in interval notation.

Front

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

Back

The domain is (-∞, 0) U (0, ∞) because x cannot be 0.

Front

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

Back

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