Relations, Functions, Domain and Range

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).

Front

What is a function?

Back

A function is a special type of relation where each input (x-value) is associated with exactly one output (y-value).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is repeated with different y-values.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph represents a function by checking if any vertical line crosses the graph more than once.

Front

What is an example of a function?

Back

y = 2x + 3 is a function because for every x-value, there is exactly one y-value.

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What is an example of a relation that is not a function?

Back

The relation {(1, 2), (1, 3)} is not a function because the x-value 1 is associated with two different y-values.

Front

What is the notation for domain?

Back

The domain is often expressed in interval notation, such as (-7, 5) or using inequalities like -7 ≤ x < 5.