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The vertical line test, shown graphically. The abscissa shows the domain of the (to be tested) function. 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.
Schematic depiction of a function described metaphorically as a "machine" or "black box" that for each input yields a corresponding output The red curve is the graph of a function, because any vertical line has exactly one crossing point with the curve. A function f from a set X to a set Y is an assignment of one element of Y to each element of X.
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 ...
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 ...
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5 potentially merging Horizontal line test and Vertical line test into monotonicity?
In chemistry, the vertical line is used in cell notation of electrochemical cells. Example, Zn | Zn 2+ || Cu 2+ | Cu Single vertical lines show components of the cell which do not mix, usually being in different phases. The double vertical line ( || ) is used to represent salt bridge; which is used to allow free moving ions to move.
SwiftTok is abuzz with the "green line test" in efforts to analyze Taylor Swift and Travis Kelce's relationship. However, the origins of this relationship analysis method are important to note, as ...