Properties of Continuous & Discrete Relations

Front

What is a function?

Back

A function is a relation where each input (x) has exactly one output (y).

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What is the domain of a relation?

Back

The domain is the set of all possible input values (x) for a function.

Front

What is the range of a relation?

Back

The range is the set of all possible output values (y) for a function.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every x-value is paired with exactly one y-value.

Front

What does it mean for a relation to be discrete?

Back

A discrete relation consists of distinct, separate points, often represented as ordered pairs.

Front

What does it mean for a relation to be continuous?

Back

A continuous relation can be graphed with a line or curve, with no breaks or gaps.

Front

What is an example of a discrete relation?

Back

An example of a discrete relation is the set of points (1,2), (2,3), (3,4).

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What is an example of a continuous relation?

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An example of a continuous relation is the graph of the function y = x^2.

Front

What is the vertical line test?

Back

The vertical line test determines if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.

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What is the significance of the range in a function?

Back

The range indicates all possible output values that a function can produce.