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A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly ...
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
In geometry, the perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or both. The distance from a point to a line is the distance to the nearest point on that line. That is the point at which a segment from it to the given point is perpendicular to the line.
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 ...
A linear function is a polynomial functionin which the variablexhas degree at most one:[2] f(x)=ax+b{\displaystyle f(x)=ax+b}. Such a function is called linearbecause its graph, the set of all points (x,f(x)){\displaystyle (x,f(x))}in the Cartesian plane, is a line. The coefficient ais called the slopeof the function and of the line (see below).
An ordered pair of vertices, such as an edge in a directed graph. An arrow (x, y) has a tail x, a head y, and a direction from x to y; y is said to be the direct successor to x and x the direct predecessor to y. The arrow (y, x) is the inverted arrow of the arrow (x, y). articulation point A vertex in a connected graph whose removal would ...
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The graph of a degree 1 polynomial (or linear function) f(x) = a0 + a1x, where a1 ≠ 0, is an oblique line with y-intercept a0 and slope a1. The graph of a degree 2 polynomial. f(x) = a0 + a1x + a2x2, where a2 ≠ 0. is a parabola. The graph of a degree 3 polynomial. f(x) = a0 + a1x + a2x2 + a3x3, where a3 ≠ 0.