Vertical Line Test

Front

What is the Vertical Line Test?

Back

A method 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 not a function using the Vertical Line Test?

Back

If a vertical line can be drawn that intersects the graph at more than one point, then the graph is not 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 relation that is not a function?

Back

The equation x^2 + y^2 = 1 is not a function because for some x-values, there are two corresponding y-values.

Front

What does it mean for a graph to pass the Vertical Line Test?

Back

It means that for every vertical line drawn on the graph, it intersects the graph at most once, indicating that the graph represents a function.

Front

Can a horizontal line test determine if a relation 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 the difference between a function and a non-function?

Back

A function has one output for each input, while a non-function may have multiple outputs for a single input.

Front

What is a common misconception about functions?

Back

A common misconception is that all equations represent functions; however, some equations can represent relations that are not functions.

Front

What is the significance of the Vertical Line Test in mathematics?

Back

It provides a visual way to determine if a graph represents a function, which is fundamental in understanding relations.