Function vs. Non-function

Front

What is a function?

Back

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

Front

What is a non-function?

Back

A relation where at least one input (x-value) matches with more than one output (y-value).

Front

Is the relation {(1,2), (2,3), (3,4)} a function?

Back

Yes, because each input has exactly one output.

Front

Is the relation {(1,2), (1,3), (2,4)} a function?

Back

No, because the input '1' has two different outputs (2 and 3).

Front

What is the vertical line test?

Back

A method to determine if a relation is a function by checking if a vertical line intersects the graph at more than one point.

Front

Give an example of a function.

Back

f(x) = 2x + 3 is a function because for every x, there is one corresponding y.

Front

Give an example of a non-function.

Back

The relation {(1,2), (1,3)} is a non-function because the input '1' has two outputs.

Front

What does it mean for a relation to be one-to-one?

Back

A one-to-one relation is a function where each output is paired with exactly one input.

Front

What is a mapping diagram?

Back

A visual representation that shows how each input is paired with an output.

Front

What is the domain of a function?

Back

The set of all possible input values (x-values) for the function.