Domain and Range of Functions (Review)

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 based on its domain.

Front

How do you determine the range from a graph?

Back

To determine the range from a graph, identify the lowest and highest points on the y-axis that the graph reaches.

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) that the function can accept.

Front

How do you determine the domain from a graph?

Back

To determine the domain from a graph, identify the leftmost and rightmost points on the x-axis that the graph reaches.

Front

What does the notation -3 < x ≤ 3 mean?

Back

This notation means that x can take any value greater than -3 and up to and including 3.

Front

What does the notation -8 ≤ y ≤ 2 mean?

Back

This notation means that y can take any value from -8 to 2, including both endpoints.

Front

If a function has a range of -3 ≤ y < 1, what does this imply about its outputs?

Back

This implies that the outputs of the function can be any value from -3 up to but not including 1.

Front

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

Back

Closed intervals include the endpoints (e.g., [a, b]), while open intervals do not include the endpoints (e.g., (a, b)). This affects the values that can be included in the domain or range.

Front

How can you express the range of a function that outputs values from 1 to 5, including both endpoints?

Back

The range can be expressed as 1 ≤ y ≤ 5.

Front

What is the difference between a function's domain and its range?

Back

The domain refers to the input values (x-values), while the range refers to the output values (y-values) of the function.