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  2. Graph of a function - Wikipedia

    en.wikipedia.org/wiki/Graph_of_a_function

    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.

  3. Elliptic curve - Wikipedia

    en.wikipedia.org/wiki/Elliptic_curve

    Graphs of curves y 2 = x 3 − x and y 2 = x 3 − x + 1. Although the formal definition of an elliptic curve requires some background in algebraic geometry, it is possible to describe some features of elliptic curves over the real numbers using only introductory algebra and geometry.

  4. Asymptote - Wikipedia

    en.wikipedia.org/wiki/Asymptote

    The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) A curve intersecting an asymptote infinitely many times In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance between the curve and the line approaches zero as one or ...

  5. Division polynomials - Wikipedia

    en.wikipedia.org/wiki/Division_polynomials

    Using the relation between and +, along with the equation of the curve, the functions , , +, are all in []. Let p > 3 {\displaystyle p>3} be prime and let E : y 2 = x 3 + A x + B {\displaystyle E:y^{2}=x^{3}+Ax+B} be an elliptic curve over the finite field F p {\displaystyle \mathbb {F} _{p}} , i.e.,

  6. Implicit curve - Wikipedia

    en.wikipedia.org/wiki/Implicit_curve

    In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation x 2 + y 2 = 1 {\displaystyle x^{2}+y^{2}=1} .

  7. Linear function (calculus) - Wikipedia

    en.wikipedia.org/wiki/Linear_function_(calculus)

    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, (+) = +.

  8. Tupper's self-referential formula - Wikipedia

    en.wikipedia.org/wiki/Tupper's_self-referential...

    The formula is a general-purpose method of decoding a bitmap stored in the constant , and it could be used to draw any other image. When applied to the unbounded positive range 0 ≤ y {\displaystyle 0\leq y} , the formula tiles a vertical swath of the plane with a pattern that contains all possible 17-pixel-tall bitmaps.

  9. Singular point of a curve - Wikipedia

    en.wikipedia.org/wiki/Singular_point_of_a_curve

    If the coefficient of x 2, + +, is 0 but the coefficient of x 3 is not then the origin is a point of inflection of the curve. If the coefficients of x 2 and x 3 are both 0 then the origin is called point of undulation of the curve. This analysis can be applied to any point on the curve by translating the coordinate axes so that the origin is at ...