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-value) and an output (y-value).

Front

What is a function?

Back

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

Front

What does it mean for a relation to NOT be a function?

Back

A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

Front

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, the graph is not a function.

Front

What is the domain of a relation?

Back

The domain is the set of all possible input values (x-values) for the relation.

Front

What is the range of a relation?

Back

The range is the set of all possible output values (y-values) for the relation.

Front

Given the relation {(1,2), (2,3), (3,4)}, is it a function?

Back

Yes, because each x-value has only one corresponding y-value.

Front

Given the relation {(1,2), (1,3), (2,4)}, is it a function?

Back

No, because the x-value 1 has two different y-values (2 and 3).

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represents a point in a coordinate system.

Front

What is the difference between a function and a relation?

Back

All functions are relations, but not all relations are functions. Functions have a unique output for each input.