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 determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

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

Back

A relation is not a function if at least one x-value is paired with more than one y-value.

Front

What is the vertical line test?

Back

A method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

What is a mapping diagram?

Back

A visual representation of a function that shows how each input is paired with an output.

Front

If a relation has the pairs (2, 3), (2, 4), (3, 5), is it a function?

Back

No, because the x-value 2 has two different y-values (3 and 4).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

What is an example of a function?

Back

The relation {(1, 2), (2, 3), (3, 4)} is a function because each x-value has one y-value.

Front

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

Back

The relation {(1, 2), (1, 3), (2, 4)} is not a function because the x-value 1 has two y-values (2 and 3).