Function vs Not a Function

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 the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph more than once, it is not a function.

Front

What does it mean if a graph passes the vertical line test?

Back

If a graph passes the vertical line test, it means that for every x-value, there is only one corresponding y-value, confirming it is 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

What is an example of a function?

Back

An example of a function is the equation y = 2x + 3, where each x-value has a unique y-value.

Front

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

Back

An example of a relation that is not a function is the equation y^2 = x, where each x-value can correspond to two y-values.

Front

What does it mean if a graph does not pass the vertical line test?

Back

If a graph does not pass the vertical line test, it means that at least one x-value has multiple corresponding y-values, indicating it is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one. If any horizontal line intersects the graph more than once, the function is not one-to-one.

Front

Can a vertical line be a function?

Back

No, a vertical line is not a function because it has multiple y-values for the same x-value.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.