Function vs. Non-function

Front

What is a function?

Back

A function is a relation where every 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

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

Back

No, because the input '1' has two outputs: '2' and '3'.

Front

Is the set {(3, 4), (5, 6), (7, 8)} a function?

Back

Yes, because each input has a unique output.

Front

What does it mean for a relation to be a function?

Back

It means that for every input, there is only one corresponding output.

Front

Which of the following is NOT a function: {(1, 2), (2, 3), (2, 4)}?

Back

It is not a function because the input '2' has two outputs: '3' and '4'.

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

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is an example of a function?

Back

The relation {(1, 2), (2, 3), (3, 4)} is a function because each input has a unique output.

Front

What is an example of a non-function?

Back

The relation {(1, 2), (1, 3), (2, 4)} is a non-function because the input '1' has two outputs.