Vertical Line Test

Front

What is the Vertical Line Test?

Back

A method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What does it mean for a relation to be a function?

Back

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

Front

How can you tell if a graph is a function using the Vertical Line Test?

Back

If a vertical line drawn anywhere on the graph intersects it at more than one point, then the graph is not a function.

Front

What is an example of a function?

Back

The graph of y = x^2 is a function because it passes the vertical line test.

Front

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

Back

The graph of a circle, such as x^2 + y^2 = r^2, is not a function because a vertical line can intersect it at two points.

Front

What does it mean if a graph passes the Vertical Line Test?

Back

It means that for every x-value, there is only one corresponding y-value, confirming it is a function.

Front

Can a straight line be a function?

Back

Yes, a straight line can be a function if it is not vertical.

Front

What is the significance of the Horizontal Line Test?

Back

The Horizontal Line Test determines if a function is one-to-one, meaning each y-value corresponds to only one x-value.

Front

What is a non-function graph?

Back

A graph that fails the vertical line test, meaning it has at least one x-value with multiple y-values.

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.