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.

Back

An example of a function is the relation {(1, 2), (2, 3), (3, 4)} where each x-value has a unique y-value.

Front

Give an example of a non-function.

Back

An example of a non-function is the relation {(1, 2), (1, 3), (2, 4)} where the x-value 1 has two different y-values.

Front

What does it mean for a relation to have repeating input values?

Back

Repeating input values means that the same x-value is paired with multiple y-values, which indicates that the relation is not a function.

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 diagram represents a function?

Back

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

Front

What is the significance of the x-value in a function?

Back

The x-value (input) in a function determines the corresponding y-value (output). Each x-value must map to only one y-value.

Front

What happens if a function has two outputs for the same input?

Back

If a function has two outputs for the same input, it is not a function because it violates the definition of a function.