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"x^y = y^x - commuting powers". Arithmetical and Analytical Puzzles. Torsten Sillke. Archived from the original on 2015-12-28. dborkovitz (2012-01-29). "Parametric Graph of x^y=y^x". GeoGebra. OEIS sequence A073084 (Decimal expansion of −x, where x is the negative solution to the equation 2^x = x^2)
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.
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).
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 ...
The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.
The graphs of y = f(x) and y = f −1 (x). The dotted line is y = x. If f is invertible, then the graph of the function = is the same as the graph of the equation = (). This is identical to the equation y = f(x) that defines the graph of f, except that the roles of x and y have
Hence the constant "k" is the product of x and y. The graph of two variables varying inversely on the Cartesian coordinate plane is a rectangular hyperbola. The product of the x and y values of each point on the curve equals the constant of proportionality (k). Since neither x nor y can equal zero (because k is non-zero), the graph never ...
The y-intercept is the initial value = = at =. The slope a measures the rate of change of the output y per unit change in the input x. In the graph, moving one unit to the right (increasing x by 1) moves the y-value up by a: that is, (+) = +.