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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]
Test of vertical wavy line with specified dimensions. Converted from the following vector PostScript source code: <pre>%! 10 setlinewidth 20 0 moveto 0 30 -10 45 -10 75 rcurveto 0 30 10 45 10 75 rcurveto 0 30 -10 45 -10 75 rcurveto 0 30 10 45 10 75 rc...
Given a function : (i.e. from the real numbers to the real numbers), we can decide if it is injective by looking at horizontal lines that intersect the function's graph. If any horizontal line = intersects the graph in more than one point, the function is not injective. To see this, note that the points of intersection have the same y-value ...
In general, implicit curves fail the vertical line test (meaning that some values of x are associated with more than one value of y) and so are not necessarily graphs of functions. However, the implicit function theorem gives conditions under which an implicit curve locally is given by the graph of a function (so in particular it has no self ...
The term "horizontal line test" is sometimes used in calculus (it is the same idea as Vertical line test).However, this article is written in very general terms and is claimed to be part of set theory, which doesn't make any sense to me, because the bit about graphs and horizontal lines seems to require a real-valued function of a real variable.
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In relational database theory, a functional dependency is the following constraint between two attribute sets in a relation: Given a relation R and attribute sets ,, X is said to functionally determine Y (written X → Y) if each X value is associated with precisely one Y value.
In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. [1] The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change ...