| 词条 | Vertical line test |
| 释义 |
In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x. If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.[1] To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y-axis for any chosen value of x. If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function. If, alternatively, a vertical line intersects the graph no more than once, no matter where the vertical line is placed, then the graph is the graph of a function. For example, a curve which is any straight line other than a vertical line will be the graph of a function. As another example, a sideways parabola (one whose directrix is a vertical line) is not the graph of a function because some vertical lines will intersect the parabola twice. See also
Notes1. ^{{cite book | last = Stewart | first = James | title = Calculus: Concepts and Contexts |edition=2nd |page=17 | publisher = Brooks/Cole | location = Pacific Grove | year = 2001 | isbn = 978-0-534-37718-2 |quote=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.}} 1 : Functions and mappings |
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