Vertical Line Test

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is 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 defines a function in mathematical terms?

Back

A function is a relation in which each input (or x-value) is associated with exactly one output (or y-value).

Front

How can you tell if a graph is not a function?

Back

A graph is not a function if a vertical line drawn through the graph intersects it at more than one point.

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 circle equation x^2 + y^2 = r^2, as it fails the vertical line test.

Front

What does it mean for a graph to pass the vertical line test?

Back

For a graph to pass the vertical line test, it must not be intersected by any vertical line at more than one point.

Front

Can a horizontal line test determine if a function is one-to-one?

Back

Yes, the horizontal line test can determine 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

What is the difference between a function and a relation?

Back

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

Front

What is an example of a function?

Back

An example of a function is the equation y = 2x + 3, which produces a unique y-value for every x-value.

Front

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

Back

In calculus, the vertical line test is significant for determining the validity of functions before applying concepts like limits and derivatives.

Front

How can you visually identify a function from a graph?

Back

You can visually identify a function from a graph by checking if any vertical line drawn through the graph intersects it at only one point.