Function vs. Relation

Front

What is a function?

Back

A relation where every input (x-value) matches with exactly one output (y-value).

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 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 the horizontal line test?

Back

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

Front

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

Back

If at least one input corresponds to more than one output.

Front

Give an example of a function.

Back

The equation y = 2x + 3 is a function because for every x, there is exactly one y.

Front

Give an example of a relation that is not a function.

Back

The set of ordered pairs {(1, 2), (1, 3)} is not a function because the input 1 corresponds to two different outputs.

Front

What is an ordered pair?

Back

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

Front

What is a mapping?

Back

A way to describe how each input is paired with an output in a relation.

Front

What is a linear function?

Back

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