Identifying Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What does it mean for a mapping to represent a function?

Back

A mapping represents a function if each input is paired with exactly one output.

Front

How can you tell if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if no two pairs have the same first element with different second elements.

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

Does the following mapping represent a function? {(1, 2), (1, 3)}

Back

No, because the input '1' is paired with two different outputs.

Front

Does the following table represent a function? Input: 1, 2, 3 Output: 4, 4, 5

Back

Yes, because each input has exactly one output.

Front

Does the following graph represent a function? (0, 1), (1, 2), (2, 3), (3, 4)

Back

Yes, because each x-value is unique.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation {(1, 2), (1, 3)}.

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 definition of a one-to-one function?

Back

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