Function vs Non Function

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is a non-function?

Back

A non-function is a relation where at least one input (x-value) has more than one output (y-value).

Front

How can you tell 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, it is not a function.

Front

What does the vertical line test involve?

Back

The vertical line test involves drawing vertical lines through a graph; if any vertical line crosses the graph at more than one point, the graph is not a function.

Front

Give an example of a function using ordered pairs.

Back

{(1,2), (2,3), (3,4)} is a function because each x-value is unique.

Front

Give an example of a non-function using ordered pairs.

Back

{(1,2), (1,3), (2,4)} is not a function because the x-value '1' has two different y-values.

Front

What is the definition of an ordered pair?

Back

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

Front

What is the significance of x-values in a function?

Back

In a function, each x-value must be unique; no x-value can correspond to more than one y-value.

Front

What is the significance of y-values in a function?

Back

In a function, y-values can repeat, but each y-value must correspond to only one x-value.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, which can be a function or a non-function.