## Definition of linear function

Function or a functional unit is defined as the association between a set of inputs and set of outputs. It can be defined as the relation of objects. When a function is defined there exists at least one value in the output set for value in an input set and if a function is one- one function then there exists exactly one value or one output for every input.

A function is of many types that are real functions, scalar functions, vector function, complex function, and a linear function. **Linear function definition** can be given as if it satisfies two main properties. First one among it is when f(a * x) is equals to a * f(x) where 'a' is a constant and 'x' is a variable and second property is given by f (x + y) is equals to f(x) + f(y). if a function satisfies these properties then it is said to be satisfying a linear function.

It is a single degree function and thus can also be considered as a polynomial function as it is represented by f (x) it is termed as a function of 'x'. A linear function is also a algebraic function in which a term is either in a form of product of constant or a constant or a single variable. For representation of a linear function if the coordinates are given then it can be expressed in the form of function and similarly opposite also exists that is if a function is given then coordinates can be determined. For example, if the coordinate is given as (4, 16) then function for this coordinate will be f (4) which is equals to 16. And graphically also it can be easily represented.

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## linear function definition

In this blog we will discuss the **linear function definition**. Linear Functions are those functions whose graphs made up of sections of one straight line throughout the function’s domain.

Linear function is describe as the functions that have ‘p’ as input variable and ‘p’ has an exponent of only 1.

Linear functions can follow to the following conditions:

A polynomial first degree function has one variable.

A mapping among two vector spaces that ascribe vector addition.

It is also said to be linear because the graphs of these functions in the cartesian co- ordinate is straight line. We will understand it with the help of small example:

Suppose we have given some functions below which has graph that is a straight line.

F (p) = 2p + 4,

F (p) = p / 2 – 3.

It can also be written in following manner as:

f (p) = mp + b,

(y – y1) = m (x – x1),

0 = Ax + By + C.

In the case of vector Algebra a linear function means that a linear map that is a map between two vectors spaces where refers vector addition and scalar multiplication.

The linear functions are those functions ‘f’ which can be represented as,

f (p) = Kp, here ‘K’ is a matrix.

A function F (p) = mp + b is said to be a linear map if and only if value of b = 0.

The form y = mx + b is named as the slope intercept form of linear function. For a common graph (p, q) usually expressed as q = mp + b and in a formal function definition a linear function written as f (x) = mx + b. In this we can easily solve any function.

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