Identifying Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

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

Back

A set of ordered pairs represents a function if no two different pairs have the same first element (input).

Front

What does it mean if a table does not represent a function?

Back

It means that at least one input is associated with more than one output.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between inputs and outputs, showing how each input is paired with an output.

Front

How can you tell if a mapping represents a function?

Back

A mapping represents a function if each input is connected to only one output.

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

What does it mean if a graph represents a function?

Back

It means that for every x-value (input), there is exactly one y-value (output).

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

Front

What is an example of a function?

Back

An example of a function is f(x) = x + 2, where each input x has 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 is associated with two different outputs.