Domain and Range Practice

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

What does it mean when we say a graph goes down to -∞?

Back

It means that the lowest point of the graph extends indefinitely downward, indicating that there is no minimum value.

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) that the function can accept.

Front

What does the notation \( (-\infty, 5] \) represent?

Back

This notation indicates that the domain or range includes all values less than or equal to 5, extending infinitely to the left.

Front

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

Back

To determine the RANGE, identify the lowest and highest points on the graph and note the y-values they correspond to.

Front

What does it mean when a graph goes to \( \infty \)?

Back

It means that the graph extends indefinitely upward, indicating that there is no maximum value.

Front

What is the significance of the interval notation \( [1, \infty) \)?

Back

This notation indicates that the range starts at 1 and includes all values greater than 1, extending indefinitely to the right.

Front

How can you find the DOMAIN of a function from its graph?

Back

To find the DOMAIN, look for the x-values that the graph covers, including any restrictions such as holes or vertical asymptotes.

Front

What does the notation \( (-3, \infty) \) indicate about the DOMAIN?

Back

This notation indicates that the domain includes all values greater than -3, but not -3 itself.

Front

What is the difference between open and closed intervals?

Back

Open intervals (e.g., \( (a, b) \)) do not include endpoints, while closed intervals (e.g., \( [a, b] \)) include endpoints.