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The points P 1, P 2, and P 3 (in blue) are collinear and belong to the graph of x 3 + 3 / 2 x 2 − 5 / 2 x + 5 / 4 . The points T 1, T 2, and T 3 (in red) are the intersections of the (dotted) tangent lines to the graph at these points with the graph itself. They are collinear too.
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.
Alternatively, replace the 3n + 1 with n ′ / H(n ′) where n ′ = 3n + 1 and H(n ′) is the highest power of 2 that divides n ′ (with no remainder). The resulting function f maps from odd numbers to odd numbers. Now suppose that for some odd number n, applying this operation k times yields the number 1 (that is, f k (n) = 1).
A cycle graph or circular graph of order n ≥ 3 is a graph in which the vertices can be listed in an order v 1, v 2, …, v n such that the edges are the {v i, v i+1} where i = 1, 2, …, n − 1, plus the edge {v n, v 1}. Cycle graphs can be characterized as connected graphs in which the degree of all vertices is 2.
An example with three indeterminates is x 3 + 2xyz 2 − yz + 1. ... The graph of a degree 1 polynomial (or linear function) f(x) = a 0 + a 1 x, where a 1 ≠ 0,
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. [1] The set X is called the domain of the function [2] and the set Y is called the codomain of the function. [3] Functions were originally the idealization of how a varying quantity depends on another quantity.
This is a 3-regular graph with 56 vertices and 84 edges, named after Felix Klein. It is Hamiltonian, has chromatic number 3, chromatic index 3, radius 6, diameter 6 and girth 7. It is also a 3-vertex-connected and a 3-edge-connected graph. It has book thickness 3 and queue number 2. [1]
1.1.3 Curves with genus > 1. 1.1.4 Curve families with variable genus. 1.2 Transcendental curves. 1.3 Piecewise constructions. 1.4 Fractal curves. 1.5 Space curves ...