Identifying Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is only one corresponding y-value.

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 pairs have the same first element (x-value) with different second elements (y-values).

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, then the graph does not represent a function.

Front

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

Back

A graph represents a function if each x-value has only one corresponding y-value.

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 a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its output.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

Give an example of a function using ordered pairs.

Back

Example: {(1, 2), (2, 3), (3, 4)} is a function because each x-value (1, 2, 3) has a unique y-value (2, 3, 4).

Front

Give an example of a relation that is not a function using ordered pairs.

Back

Example: {(1, 2), (1, 3), (2, 4)} is not a function because the x-value 1 is associated with two different y-values (2 and 3).

Front

What is the domain of a function?

Back

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