Domain and Range from a Graph

Front

What is the definition of Domain in a graph?

Back

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

Front

What is the definition of Range in a graph?

Back

The range of a function is the complete set of possible values of the dependent variable (y-values) that the function can output.

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. This includes all x-values for which there is a corresponding y-value.

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. This includes all y-values that correspond to the x-values in the domain.

Front

What does the notation (-∞, ∞) represent?

Back

The notation (-∞, ∞) represents that the domain includes all real numbers from negative infinity to positive infinity.

Front

What does the notation [-2, 3] represent?

Back

The notation [-2, 3] indicates that the domain includes all real numbers from -2 to 3, including the endpoints -2 and 3.

Front

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

Back

Closed intervals, denoted by brackets [ ], indicate that the endpoints are included in the set of values.

Front

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

Back

Open intervals, denoted by parentheses ( ), indicate that the endpoints are not included in the set of values.

Front

If a graph has a horizontal line at y = 2, what can be said about its range?

Back

The range includes the value y = 2, and may also include other y-values depending on the graph's behavior.

Front

How can vertical asymptotes affect the domain of a function?

Back

Vertical asymptotes indicate values of x where the function is undefined, thus those x-values are excluded from the domain.