Function or Not a Function

Front

What is a function?

Back

A function is a relation where each input has exactly 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 relation is not a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

Example of a function: y = 2x + 3. Is this a function?

Back

Yes, because for every x value, there is exactly one y value.

Front

Example of a relation: {(1, 2), (1, 3), (2, 4)}. Is this a function?

Back

No, because the input '1' is associated with two different outputs (2 and 3).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

If a graph passes the vertical line test, what can we conclude?

Back

We can conclude that the graph represents a function.

Front

What is an example of a non-function?

Back

A circle is an example of a non-function because it fails the vertical line test.

Front

What is a one-to-one function?

Back

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