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, it is not a function.

Front

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

Back

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

Front

If a vertical line intersects a graph at two points, what can we conclude?

Back

The graph does not represent a function.

Front

What is an example of a function?

Back

The equation y = 2x + 3 represents a function because for every x-value, there is one unique y-value.

Front

What is an example of a non-function?

Back

The equation x^2 + y^2 = 1 is not a function because a vertical line can intersect it at two points.

Front

How can you visually identify a function using a graph?

Back

By applying the vertical line test; if any vertical line crosses the graph more than once, it is not a function.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Can a vertical line ever represent a function?

Back

No, a vertical line does not represent a function because it fails the vertical line test.

Front

What is the significance of the vertical line test in mathematics?

Back

It helps to quickly determine if a relation is a function without needing to analyze the entire equation.