Domain & Range (from graphs, functions, and applications)

Front

What is the definition of Domain in a function?

Back

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

Front

What is the definition of Range in a function?

Back

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

Front

How do you express the domain of a function in interval notation?

Back

Use brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints.

Front

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

Back

The domain is [0, ∞) because the square root function is only defined for non-negative numbers.

Front

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

Back

The range is [0, ∞) because the output of a square function is always non-negative.

Front

If a function has a domain of [1, 5], what does this mean?

Back

The function is defined for all x-values from 1 to 5, including 1 and 5.

Front

What is the range of a function that models the height of a ball thrown into the air?

Back

The range is all real numbers between 0 and the maximum height of the ball.

Front

How do you determine the reasonable domain for a real-world situation?

Back

Consider the context of the situation and identify the values that make sense (e.g., time cannot be negative).

Front

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

Back

The domain is all real numbers except x = 0, expressed as (-∞, 0) U (0, ∞).

Front

What does it mean if a function has a range of (-∞, 5]?

Back

The function can produce any output value less than or equal to 5.