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

What is the domain of a function?

Back

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

Front

How can you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph of the relation at more than one point, then the relation is not a function.

Front

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

Back

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

Front

What is an example of a function?

Back

f(x) = 2x + 3 is a function because for every x, there is exactly one y.

Front

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 input 1 is associated with two different outputs.

Front

What is the difference between discrete and continuous functions?

Back

Discrete functions have distinct, separate values, while continuous functions have values that form a continuous line or curve.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between the domain and range of a function.