Relations and Functions

Front

What is a Relation in mathematics?

Back

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

Front

What is a Function?

Back

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

Front

How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (x-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

Given the relation {(1, 2), (2, 3), (3, 4)}, what is the Domain?

Back

The domain is {1, 2, 3}.

Front

Given the relation {(1, 2), (2, 3), (3, 4)}, what is the Range?

Back

The range is {2, 3, 4}.

Front

What is the difference between a Relation and a Function?

Back

A relation can have multiple outputs for a single input, while a function has only one output for each input.

Front

Is the set {(2, 3), (2, 4), (3, 5)} a function?

Back

No, because the input 2 has two different outputs (3 and 4).

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input.