Relations and Functions

Front

What is the definition of 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 the definition of a function?

Back

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

Front

Identify the domain of the relation: {(-6,14), (0,32), (2,38), (4,44)}

Back

{-6, 0, 2, 4}.

Front

Identify the range of the relation: {(-6,14), (0,32), (2,38), (4,44)}

Back

{14, 32, 38, 44}.

Front

What is the domain of a function?

Back

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

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 an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value corresponds to one y-value.

Front

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

Back

An example of a relation that is not a function is {(1,2), (1,3)}, where the input 1 corresponds to two different outputs.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output value (y) is associated with exactly one input value (x).