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

How is interval notation used to represent domain and range?

Back

Interval notation uses brackets [ ] to include endpoints and parentheses ( ) to exclude endpoints.

Front

What does the interval notation [-3, 1) represent?

Back

This notation represents all real numbers x such that -3 ≤ x < 1.

Front

What does the interval notation (-∞, 4] represent?

Back

This notation represents all real numbers x such that x ≤ 4.

Front

What is the domain of the function f(x) = √(x - 2)?

Back

The domain is [2, ∞) 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 found by identifying values that make the denominator zero and excluding them.

Front

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

Back

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

Front

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

Back

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