particularly in game theory and mathematical economics, a function is graph continuous if its graph—the set of all input-output pairs—is a closed set in the...

In mathematics, a real function f {\displaystyle f} of real numbers is said to be uniformly continuous if there is a positive real number δ {\displaystyle...

exists a real number such that, for every pair of points on the graph of this function, the absolute value of the slope of the line connecting them is...

differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable...

a subset of three-dimensional space; for a continuous real-valued function of two real variables, its graph forms a surface, which can be visualized as...

(Rademacher's theorem). When we try to draw a general continuous function, we usually draw the graph of a function which is Lipschitz or otherwise well-behaved...

mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies...

or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are...

function is a real-valued function of a real variable, whose graph is composed of straight-line segments. A piecewise linear function is a function defined...

mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs. Each gives conditions...

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in...

topology, closed graph is a property of functions. A function f : X → Y between topological spaces has a closed graph if its graph is a closed subset...

parameters, their graph can have only very few shapes. In fact, the graph of a cubic function is always similar to the graph of a function of the form y =...

as the graph of a function. There may not be a single function whose graph can represent the entire relation, but there may be such a function on a restriction...

integer. Constant function: polynomial of degree zero, graph is a horizontal straight line Linear function: First degree polynomial, graph is a straight line...

real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between...

The graphs below show examples of hypothetical survival functions. The x-axis is time. The y-axis is the proportion of subjects surviving. The graphs show...

For the graph of a function f of differentiability class C2 (its first derivative f', and its second derivative f'', exist and are continuous), the condition...

is they are continuous, differentiable, and even analytic. This regularity insures that these functions can be visualized by their graphs. In this section...

piecewise linear, piecewise smooth, piecewise continuous, and others are also very common. The meaning of a function being piecewise P {\displaystyle P} , for...

set. Boundedness can also be determined by looking at a graph.[citation needed] The sine function sin : R → R {\displaystyle \sin :\mathbb {R} \rightarrow...

those y ∈ Y with (x,y) ∈ Γf. If f is an ordinary function, it is a multivalued function by taking its graph Γ f   =   { ( x , f ( x ) )   :   x ∈ X } . {\displaystyle...

or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) F : R → [ 0 , 1 ] {\displaystyle...

integer. Even functions are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose graph is self-symmetric...

of the function. Geometrically, a periodic function can be defined as a function whose graph exhibits translational symmetry, i.e. a function f is periodic...

sublinear function on X . {\displaystyle X.} Then the following are equivalent: p {\displaystyle p} is continuous; p {\displaystyle p} is continuous at 0;...

along x-axis, traveled by a point moving along the graph has a finite value. For a continuous function of several variables, the meaning of the definition...

bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the...

technique, the graph appears as a set of dots. The values of a variable measured in continuous time are plotted as a continuous function, since the domain...

} If the function maps real numbers to real numbers, then its zeros are the x {\displaystyle x} -coordinates of the points where its graph meets the...