Functions vs. Non-Functions

Front

What is a function?

Back

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

Front

What is a non-function?

Back

A non-function is a relation where at least one input (x-value) has more than one output (y-value).

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

Give an example of a function using ordered pairs.

Back

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

Front

Give an example of a non-function using ordered pairs.

Back

{(1, 2), (1, 3), (2, 4)} is a non-function because the x-value 1 has two different y-values.

Front

What does it mean for a relation to be one-to-one?

Back

A one-to-one relation is a function where each x-value maps to a unique y-value and each y-value is paired with only one x-value.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How can you tell if a graph is a function?

Back

You can tell if a graph is a function by using the vertical line test.

Front

What is an example of a function in real life?

Back

An example of a function in real life is a vending machine, where each button (input) corresponds to one specific item (output).