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Roots and y-intercept in red; Vertex and axis of symmetry in blue; Focus and directrix in pink; Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex (orange). Its x-intercepts are rotated 90° around their mid-point, and the Cartesian plane is interpreted as the complex plane (green). [3
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.
The graphs can be used together to determine the economic equilibrium (essentially, to solve an equation). Simple graph used for reading values: the bell-shaped normal or Gaussian probability distribution , from which, for example, the probability of a man's height being in a specified range can be derived, given data for the adult male population.
In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...
If a directed path leads from vertex x to vertex y, x is a predecessor of y, y is a successor of x, and y is said to be reachable from x. direction 1. The asymmetric relation between two adjacent vertices in a graph, represented as an arrow. 2. The asymmetric relation between two vertices in a directed path. disconnect Cause to be disconnected ...
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
One can represent any finite partial order as a family of sets, such that x < y in the partial order whenever the set corresponding to x is a subset of the set corresponding to y. In this way, comparability graphs can be shown to be equivalent to containment graphs of set families; that is, a graph with a vertex for each set in the family and ...
The least squares linear fit to this plot has an intercept of 0 and a slope , where corresponds to the regression coefficient for X i of a regression of Y on all of the covariates. The residuals from the least squares linear fit to this plot are identical to the residuals from the least squares fit of the original model (Y against all the ...