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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.
File:Y=x^3-3x^2+1.svg. Add languages. Page contents not supported in other languages. ... English: The graph of y = x 3 - 3x 2 + 1. Date: 18 November 2010: Source ...
Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis—where y = 0).The case shown has two critical points.Here the function is f(x) = (x 3 + 3x 2 − 6x − 8)/4.
The incomparability graph of a poset is the graph with vertices given by the elements of which includes an edge between two vertices if and only if their corresponding elements in are incomparable. Conjecture (Stanley–Stembridge) Let G {\displaystyle G} be the incomparability graph of a ( 3 + 1 ) {\textstyle (3+1)} -free poset, then X G ...
The graph of the function y = ƒ(x) is the set of points of the plane with coordinates (x, ... x 2 +2x+3 is a parabolic asymptote to (x 3 +2x 2 +3x+4)/x. Let A : ...
An example of a stationary point of inflection is the point (0, 0) on the graph of y = x 3. The tangent is the x-axis, which cuts the graph at this point. An example of a non-stationary point of inflection is the point (0, 0) on the graph of y = x 3 + ax, for any nonzero a. The tangent at the origin is the line y = ax, which cuts the graph at ...
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The set of all the automorphisms of a graph is a group for the composition. For both Loupekine snarks, this group is the dihedral group D 6 {\displaystyle D_{6}} (identified as [12,4] in the Small Groups Database).