Relations and Functions

Front

What is a function?

Back

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

Front

What is the vertical line test?

Back

The vertical line test is 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

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

Back

Yes, because each input has a unique output.

Front

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

Back

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

Front

What is a relation?

Back

A relation is a set of ordered pairs, which can include functions but does not have to.

Front

Which of the following is a function: {(1, 2), (2, 3), (1, 4)} or {(1, 2), (2, 3), (3, 4)}?

Back

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

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 associated with exactly one input.

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 the domain of a function?

Back

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

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for the function.