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) 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) with different second elements (y-values).

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

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 is a function by checking if any vertical line crosses the graph more than once.

Front

Given the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the domain?

Back

D: {-4, 0, 1, 2}.

Front

Given the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the range?

Back

R: {-4, -3, 1}.

Front

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

Back

The relation {(1,-5), (-1,6), (1,5), (6,-3)} is not a function because the input '1' has two different outputs (-5 and 5).