Domain and Range From Graphs

Front

What is the definition of 'domain' in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) for which the function is defined.

Front

What is the definition of 'range' in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that result from using the function.

Front

How do you determine the domain from a graph?

Back

To determine the domain from a graph, identify all the x-values that the graph covers. Look for any restrictions such as open circles or vertical asymptotes.

Front

How do you determine the range from a graph?

Back

To determine the range from a graph, identify all the y-values that the graph covers. Look for any restrictions such as open circles or horizontal asymptotes.

Front

What does an open circle on a graph indicate about the domain?

Back

An open circle indicates that the endpoint is not included in the domain, meaning the value is not part of the function.

Front

What does a closed circle on a graph indicate about the range?

Back

A closed circle indicates that the endpoint is included in the range, meaning the value is part of the function.

Front

If a graph extends infinitely to the left, what can be said about the domain?

Back

If a graph extends infinitely to the left, the domain includes all values less than or equal to the leftmost point.

Front

If a graph has a horizontal line at y = 3, what is the range?

Back

The range is y = 3, as the graph does not extend above or below this line.

Front

What is the domain of the function graphed with endpoints at x = -2 and x = 5, including both endpoints?

Back

The domain is -2 ≤ x ≤ 5.

Front

What is the range of the function graphed with a minimum point at y = 1 and extending upwards?

Back

The range is y ≥ 1.