Domain, Range, and Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is paired with more than one y-value.

Front

What is the domain of 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 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.

Front

What does it mean for a function to be defined on an interval?

Back

A function is defined on an interval if its domain includes all values between two endpoints.

Front

How do you express the domain of a function using set notation?

Back

The domain can be expressed in set notation as {x | condition}, where 'condition' describes the valid x-values.

Front

What is the significance of the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is an example of a non-function relation?

Back

An example of a non-function relation is a circle, where multiple y-values correspond to the same x-value.

Front

How can you find the domain of a graph visually?

Back

You can find the domain of a graph by identifying the x-values that the graph covers on the horizontal axis.

Front

How can you find the range of a graph visually?

Back

You can find the range of a graph by identifying the y-values that the graph covers on the vertical axis.