Identifying Functions

Front

What is a function?

Back

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

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 (x-value) with different second elements (y-values).

Front

Does the ordered pair (2, 3) and (2, 4) represent a function?

Back

No, because the input 2 has two different outputs (3 and 4).

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 has two different outputs (2 and 3).

Front

What does it mean for a relation to be not a function?

Back

A relation is not a function if at least one input is associated with more than one 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 an example of a function?

Back

An example of a function is f(x) = x + 1, where each input x gives a unique output.

Front

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

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two outputs.