Apr 30, 2014 · 1 You know that a linear function satisfies the following property: $$f (a+b)=f (a)+f (b)$$ and you want to determine whether a particular function $g$ is linear, so you just check whether this …

Mar 29, 2021 · How to prove that any linear function which is defined on a convex subset of $\\mathbb{R}^n$ attains its maximum always at one of the extreme points of the set? Thank you for …

May 20, 2015 · I would simply define a linear function as always having the same slope (and, more technically, it must be continuous). Clearly, the absolute value function has a negative slope for …

Jul 30, 2019 · Such a function may also be called a linear map. Note that this is different from the middle school definition of a linear function in two very important ways: first, the definition applies to …

Oct 30, 2017 · It depends on how you define "a linear function" The graph is a horizontal line. Often times, books describe linear functions as polynomials of degree 1, which would require a nonzero …

Question 358837: Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 15 gallons of fuel, the airplane weighs 2187 pounds.

Jun 8, 2023 · A linear function fixes the origin, whereas an affine function need not do so. An affine function is the composition of a linear function with a translation, so while the linear part fixes the …

Feb 7, 2015 · That's why I emphasized the distinction between a linear function in the context of calculus, and in the context of linear algebra and functional analysis. Although I do agree that calling …

May 16, 2020 · This definition works for linear functions but I was asking more about the specific term "linear" and how you would approach it regardless of what comes after the word linear, whether it be …

Sep 8, 2011 · I think linear refers to the fact that vector spaces are not curved. For instance, the wikipedia page for linear spaces gets redirected to the page on vector spaces. So does the one at …