In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle...

The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local maximum. Otherwise, a cubic...

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...

a 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...

curve. There are three kinds of asymptotes: horizontal, vertical and oblique. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes...

a function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function...

term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight...

curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward)...

in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is...

} 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...

advantage of drawing a graph of sine and cosine functions. This can be done by rotating counterclockwise a point along the circumference of a circle, depending...

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

on the x-axis of the graph, as the projection of the graph of the function onto the x-axis. For a function f : X → Y {\displaystyle f\colon X\to Y} , the...

of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent...

of the graph. The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative...

above formulas for the curvature. The graph of a function y = f(x), is a special case of a parametrized curve, of the form x = t y = f ( t ) . {\displaystyle...

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 not greater...

the graph of a function. Although implicit in the development of calculus of the 17th and 18th centuries, the modern idea of the limit of a function goes...

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

analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane. By...

-intercept or vertical intercept is a point where the graph of a function or relation intersects the y {\displaystyle y} -axis of the coordinate system. As such...

mathematics, the Ihara zeta function is a zeta function associated with a finite graph. It closely resembles the Selberg zeta function, and is used to relate...

test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x. If a vertical...

(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...

mathematical economics, a function is graph continuous if its graph—the set of all input-output pairs—is a closed set in the product topology of the domain and...

differentiation. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative...

raising to the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line Linear function: First degree polynomial...

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...

analysis, a function of bounded variation, also known as BV function, is a real-valued function whose total variation is bounded (finite): the graph of a function...

given a graph G = (V, E), a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph. Likewise...