Function/Not a 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 must be true for a relation to be a function?

Back

Each x value must have only one y value.

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.

Front

Can a function have repeated x-values?

Back

No, a function cannot have repeated x-values with different y-values.

Front

What does it mean if a relation is not a function?

Back

It means that at least one x-value is paired with more than one y-value.

Front

If a graph passes the vertical line test, what can we conclude?

Back

The graph represents a function.

Front

What is an example of a function?

Back

The relation {(1, 2), (2, 3), (3, 4)} is a function because each x-value has one unique y-value.

Front

What is an example of a non-function?

Back

The relation {(1, 2), (1, 3), (2, 4)} is not a function because the x-value 1 is paired with two different y-values.

Front

What is a mapping in relation to functions?

Back

A mapping shows how each input is paired with an output; for it to be a function, each input must have one output.

Front

What happens if a function has two arrows leaving one x-value?

Back

It is not a function because it violates the rule that each x-value must have only one y-value.