Explore Related Concepts


a real life application of a linear function
Best Results From Wikipedia Yahoo Answers Youtube
From Wikipedia
In mathematics, the term linear function can refer to either of two different but related concepts:
 a firstdegree polynomial function of one variable;
 a map between two vector spaces that preserves vector addition and scalar multiplication.
Analytic geometry
In analytic geometry, the term linear function is sometimes used to mean a firstdegree polynomialfunction of one variable. These functions are known as "linear" because they are precisely the functions whose graph in the Cartesian coordinate plane is a straight line.
Such a function can be written as
 f(x) = mx + b
 (yy1) = m(xx1)
 0= Ax + By + C
(called slopeintercept form), where m and b are realconstants and x is a real variable. The constant m is often called the slope or gradient, while b is the yintercept, which gives the point of intersection between the graph of the function and the yaxis. Changing m makes the line steeper or shallower, while changing b moves the line up or down.
Examples of functions whose graph is a line include the following:
 f_{1}(x) = 2x+1
 f_{2}(x) = x/2+1
 f_{3}(x) = x/21.
The graphs of these are shown in the image at right.
Vector spaces
In advanced mathematics, a linear function means a function that is a linear map, that is, a map between two vector spaces that preserves vector addition and scalar multiplication.
For example, if x and f(x) are represented as coordinate vectors, then the linear functions are those functions f that can be expressed as
 f(x) = \mathrm{M}x,
where M is a matrix. A function
 f(x) = mx + b
is a linear map if and only if b = 0. For other values of b this falls in the more general class of affine maps.
From Yahoo Answers
Answers:You might impress your teacher with a linear function that has a negative correlation  that is, as x increases, y decreases. For example  the value of your car as it increases in age.
Answers:Yes... the derivative of a function F(x) is another function f(x) that outputs the instantaneous slope of F(x) at x. Does that make sense? if y = x then y' = 2x... The parabola y=x , at every value x, has a slope of 2x I dont know how much you know about derivative calculus... but you seem to understand what it does and whats its for already. === 1) What are differential equations? DEs are equations, functions, that relate a function f(x) and its varying degrees of differentiations to each other and to other functions of x. Often times, the objective of a DE is to find out what f(x) is, explicitly, in terms of 'x'; without relating f(x) to any of its derivatives Like, for example, if the DE was: y + 2y'  x = 4 And I asked you to figure out what the function y(x) was in terms of x... The answer would not be y(x) = 4 + x  2y'(x)... because that is just the same DE rearranged. In many instances, from physics to statistics to economics... differential equations show up. DE's are equations that relate a functions output, quantity and its rate of change over the course of time 't' in a single equation... these relationships might be easy to determine with the data they have... but the mathematician might want to figure out what the quantity is at time t, or what its rate of change is... without having to know the other first
Answers:This is a classic ballistics problem and has nothing to do with football or real life. You can treat it as primarily a math problem or as a physics problem, but you need at least some bits from both. Assuming no air friction, the path of football is a parabola. You are given two points on the parabola: <0, 7> and <90, 4>. You are also given the tangent at the point <0, 7> (note that the angle is positive  y increases as x increases from 0). That defines the parabola. Part b asks what is the maximum value of y. Now you have to bring some physics into it. In the vertical direction, the path of a projectile is defined by: Vf = Vi + A T D = Vi T + (1/2) A T^2 Where: T is the time interval Vi is the initial vertical velocity Vf is the final vertical velocity D is the vertical distance traveled A is the vertical acceleration. In this case, the only acceleration is that due to gravity  approximately 32 ft/s^2 At the same time, the horizontal velocity is constant. So you have y as a function of x and y as a function of t so you can determine x as a function of t. This will also give you the initial vertical component of the velocity of the ball, and the total time the ball takes to make its trip.
Answers:One of the major processes for making formaldehyde commercially is the oxidation of methanol. Formaldehyde is an important industrial chemical used in things like plastics and insulation.
From Youtube