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A horizontal line is a straight, flat line that goes from left to right. Given a function f : R → R {\displaystyle f\colon \mathbb {R} \to \mathbb {R} } (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 .
A graphical approach for a real-valued function of a real variable is the horizontal line test. If every horizontal line intersects the curve of f ( x ) {\displaystyle f(x)} in at most one point, then f {\displaystyle f} is injective or one-to-one.
In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other. A function maps elements from its domain to elements in its codomain.
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.
The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) A curve intersecting an asymptote infinitely many times In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance between the curve and the line approaches zero as one or ...
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3 Purpose of horizontal line test? 2 comments. 4 Horizontal line test for quadrilaterals. 1 comment.
Intuitively, the graph of a bounded function stays within a horizontal band, while the graph of an unbounded function does not. In mathematics , a function f {\displaystyle f} defined on some set X {\displaystyle X} with real or complex values is called bounded if the set of its values is bounded .