Function/Not a Function

Front

What is a function?

Back

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

Front

What is the definition of 'not a function'?

Back

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

Front

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

Back

Yes, because each x-value has only one y-value paired with it.

Front

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

Back

No, because the x-value 1 has two y-values (2 and 3) paired with it.

Front

What is an example of a function?

Back

The mapping {(2, 5), (3, 6), (4, 7)} is a function because each input has one output.

Front

What is an example of a relation that is not a function?

Back

The mapping {(1, 2), (1, 3), (2, 4)} is not a 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 means that each input is paired with a unique output, and no two inputs share the same output.

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 a 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 domain of a function?

Back

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