Functions and Relations

Front

What is a function?

Back

A relation where every input (domain) has exactly one output (range).

Front

What is a relation?

Back

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

Front

What is the domain of a relation?

Back

The set of all possible input values (x-values) in a relation.

Front

What is the range of a relation?

Back

The set of all possible output values (y-values) in a relation.

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 does it mean for a mapping to be 'not a function'?

Back

It means that at least one input corresponds to more than one output.

Front

What is an example of a function?

Back

The relation {(1,2), (2,3), (3,4)} is a function because each input has one output.

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' has two different outputs.

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is a linear function?

Back

A function that graphs to a straight line, typically in the form y = mx + b.