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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.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
Graph of a linear function Graph of a polynomial function, here a quadratic function. Graph of two trigonometric functions: sine and cosine. A real function is a real-valued function of a real variable, that is, a function whose codomain is the field of real numbers and whose domain is a set of real numbers that contains an interval.
Inverse function: is declared by "doing the reverse" of a given function (e.g. arcsine is the inverse of sine). Implicit function: defined implicitly by a relation between the argument(s) and the value. Piecewise function: is defined by different expressions on different intervals. Computable function: an
The web graph W 4,2 is a cube. The web graph W n,r is a graph consisting of r concentric copies of the cycle graph C n, with corresponding vertices connected by "spokes". Thus W n,1 is the same graph as C n, and W n,2 is a prism. A web graph has also been defined as a prism graph Y n+1, 3, with the edges of the outer cycle removed. [7] [10]
In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions. Usually instructors prepare students with worked examples: the exercise is stated, then a model answer is provided. Often several worked ...
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