Domain and Range from a Graph (Exit Ticket)

Front

What is the definition of 'Domain' in 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 'Range' in 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 from a graph?

Back

To determine the domain from a graph, identify the x-values that the graph covers. Look for the leftmost and rightmost points of the graph.

Front

How do you determine the range from a graph?

Back

To determine the range from a graph, identify the y-values that the graph covers. Look for the lowest and highest points of the graph.

Front

What does it mean if a function has a domain of x < 5?

Back

It means that the function is defined for all x-values less than 5, but not including 5.

Front

What does it mean if a function has a range of y > 2?

Back

It means that the function produces y-values greater than 2, but not including 2.

Front

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

Back

An example is f(x) = √x, which has a domain of x ≥ 0 because square roots of negative numbers are not defined in the real number system.

Front

What is an example of a function with a restricted range?

Back

An example is f(x) = 1/x, which has a range of all real numbers except 0, since the function never outputs 0.

Front

How can you represent the domain and range using interval notation?

Back

Domain: (-∞, 5) for x < 5; Range: (2, ∞) for y > 2.

Front

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

Back

Open intervals (e.g., (a, b)) do not include endpoints, while closed intervals [a, b] include endpoints, indicating whether those values are part of the domain or range.