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 graph to be a function?

Back

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

Front

What does it mean for a graph to not be a function?

Back

A graph is not a function if at least one input (x-value) has more than 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

Can a horizontal line test determine if a graph is a function?

Back

No, the horizontal line test determines if a function is one-to-one, not if it is a function.

Front

What is an example of a function?

Back

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

Front

What is an example of a graph 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 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

How can you visually check if a graph is a function?

Back

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