Domain and Range

Front

What is the definition of 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 definition of 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

How do you determine the domain of a function from its graph?

Back

The domain can be determined by identifying all the x-values that the graph covers.

Front

How do you determine the range of a function from its graph?

Back

The range can be determined by identifying all the y-values that the graph covers.

Front

What does it mean if a function has a domain of all real numbers?

Back

It means that the function can accept any real number as an input.

Front

What is an example of a function with a limited domain?

Back

A function like f(x) = 1/x has a limited domain because it is undefined at x = 0.

Front

What is the significance of closed and open intervals in domain and range?

Back

Closed intervals include the endpoints, while open intervals do not. This affects whether certain values are included in the domain or range.

Front

How can you express the range of a function using set notation?

Back

The range can be expressed in set notation, such as {y | 2 < y ≤ 6}.

Front

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

Back

The domain is x ≥ 1, since 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 y ≥ 0, since the output of a square function is always non-negative.