Function vs. Non-function

Front

What is a function?

Back

A function is a relation in which each input (x-value) is associated with 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) is associated with more than one output (y-value).

Front

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

Back

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

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function. If a vertical line intersects the graph at more than one point, the relation is not a function.

Front

Given the set of pairs {(2,3), (3,4), (2,5)}, is this a function?

Back

No, because the x-value 2 has two y-values (3 and 5) associated with it.

Front

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

Back

A one-to-one function is a function where each output (y-value) is associated with exactly one input (x-value).

Front

Is the mapping {(a, b), (b, c), (c, d)} a function?

Back

Yes, because each input has a unique output.

Front

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

Back

The first set {(1,2), (2,3), (1,4)} is not a function because the x-value 1 has two y-values (2 and 4).

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).