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A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial. Its graph, when there is only one variable, is a horizontal line. In this context, a function that is also a linear map (the other meaning) may be referred to as a homogeneous linear function or a linear form.
A linear function is a polynomial function in which the variable x has degree at most one: [2] = +. Such a function is called linear because its graph, the set of all points (, ()) in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below).
The graph of this function is a line with slope and y-intercept. The functions whose graph is a line are generally called linear functions in the context of calculus. However, in linear algebra, a linear function is a function that maps a sum to the sum of the images of the summands.
Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right). In science and engineering , a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes.
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.
In mathematics, the term linear is used in two distinct senses for two different properties: . linearity of a function (or mapping);; linearity of a polynomial.; An example of a linear function is the function defined by () = (,) that maps the real line to a line in the Euclidean plane R 2 that passes through the origin.
The graph of a continuous piecewise linear function on a compact interval is a polygonal chain. (*) A linear function satisfies by definition () = and therefore in particular () =; functions whose graph is a straight line are affine rather than linear.
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope , which is a set defined as the intersection of finitely many half spaces , each of which is defined by a linear inequality.
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