Search results
Results from the WOW.Com Content Network
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.
If (x, y) is an integer point on a Mordell curve, then so is (x, −y). If (x, y) is a rational point on a Mordell curve with y ≠ 0, then so is ( x 4 − 8nx / 4y 2 , −x 6 − 20nx 3 + 8n 2 / 8y 3 ). Moreover, if xy ≠ 0 and n is not 1 or −432, an infinite number of rational solutions can be generated this way.
For example, the upper right branch of the curve y = 1/x can be defined parametrically as x = t, y = 1/t (where t > 0). First, x → ∞ as t → ∞ and the distance from the curve to the x-axis is 1/t which approaches 0 as t → ∞. Therefore, the x-axis is an asymptote of the curve.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
The equation = produces a graph where the curve and line intersect at (1, 1). The curve becomes asymptotic to 0, as opposed to 1; it is, in fact, the positive section of y = 1/ x . References
name vertices edges radius diam. girth P χ χ' 120-cell: 600: 1200: 15: 15: 5: F: 3: 4 Balaban 3-10-cage: 70: 105: 6: 6: 10: F: 2: 3 Balaban 3-11-cage: 112: 168: 6 ...
First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ··· is an elementary example of a geometric series that converges absolutely.
Given two different points (x 1, y 1) and (x 2, y 2), there is exactly one line that passes through them. There are several ways to write a linear equation of this line. If x 1 ≠ x 2, the slope of the line is . Thus, a point-slope form is [3]