Relations & Functions

Front

What is a function?

Back

A function is a relation in which each input (or domain element) is associated with exactly one output (or range element).

Front

What is a relation?

Back

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

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 (input).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph is not a function.

Front

What is the domain of a function?

Back

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

Front

Give an example of a function.

Back

Front

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

Back

The relation @@ ext{{R}} = ig\{(1,2), (1,3), (2,4)\big\ ext{{ is not a function because the input 1 is associated with two different outputs (2 and 3).}}.

Front

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

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is an ordered pair?

Back

An ordered pair is a pair of elements (a, b) where 'a' is the first element (input) and 'b' is the second element (output).