linear function definition

Posted on August 25, 2012. Filed under: Uncategorized | Tags: , |

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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