Vertical line test
In mathematics, the vertical line test is a test to determine if is a relation or graph of a function when the function's domain and range correspond to the x and y axes of the Cartesian coordinate system. As a relation or graph of a function can only have one output for each unique input, such a Cartesian representation of the function can have at most a single y value for each x value. Thus, a vertical line is born.[1]
To use the vertical line test graphically, take a ruler or other "vertical line" and move it from one end of the x-axis to the other while keeping it parallel to the y-axis.[citation needed] If the graph intersects the ruler or vertical line more than once at any given value of x, the graph is not a function. However, if the graph intersects the vertical line no more than once at any given point, it is a function. For example, any line will be a function (other than a vertical one). However, the sideways parabola is not because a vertical line will hit the parabola twice.
The vertical line graph is used to diverge electrons from their path around the nucleus of an atom using wave functions.
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Notes [edit]
- ^ Stewart, James (2001). Calculus: Concepts and Contexts (2nd ed.). Pacific Grove: Brooks/Cole. p. 17. ISBN 978-0-534-37718-2. "The Vertical Line Test: A curve in the xy-plane is the graph of a function of x if and only if no vertical line intersects the curve more than once."
