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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.
Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...
[2] This is useful in calculating moments of inertia or center of mass for a constant density, because the mass of a lamina is proportional to its area. In a case of a variable density, given by some (non-negative) surface density function ρ ( x , y ) , {\displaystyle \rho (x,y),} the mass m {\displaystyle m} of the planar lamina D is a planar ...
The graph of the logarithm to base 2 crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3). For example, log 2 (8) = 3, because 2 3 = 8. The graph gets arbitrarily close to the y axis, but does not meet or intersect it.
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 ...
Therefore, the graph of the function f(x − h) = (x − h) 2 is a parabola shifted to the right by h whose vertex is at (h, 0), as shown in the top figure. In contrast, the graph of the function f(x) + k = x 2 + k is a parabola shifted upward by k whose vertex is at (0, k), as shown in the center figure.
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 ...
The graph of a function of two variables, embedded into a three-dimensional space Topics referred to by the same term This disambiguation page lists mathematics articles associated with the same title.