Thursday, June 6, 2013

Step Functions In Math

Introduction to step function:

     A step function in math is one of the concepts of functions in math. The line is the collection of x and y points. At the same time x and y value can be increased values. We can plot this points on the graph we can get the equation of the line. That forms the step figure. So these functions are known as step functions.


Definition of Step functions in math
Definition of Step function:
    A function in the real analysis R can be defined as the step function it can be written as linear combination of semi open intervals. Open interval can be defined as [a, b) in R.  Then the step function f(x) can be described as,

f(x) =a1 f1(x) + a2 f2(x) + …………………… + an fn(x)

Brief Description of the Heaviside Step functions in math

This involves the following steps.

They are,

Step 1: First we can form the equation into y = m x + b form.

Step 2: Substitute any value for x we can get the y values.

Step 3: Plot the (x, y) points on the graph.

Step 4: This line plot increases sequentially.

Step 5: It look like as a step format.

These are the main steps used in math step functions.

Consider the equation of the line y = x -1

Substitute the values for x we can get the y values.

Substitute x=1 in the given equation y = x -1.

That is y= 1 – 1 = 0

Therefore the (x, y) co-ordinate is (1, 0)

Substitute x=2 in the given equation y = x -1.

That is y= 2 – 1 = 1

Therefore the (x, y) co-ordinate is (2, 1)

Substitute x=0 in the given equation y = x -1.

That is y= 0 – 1 = -1

Therefore the (x, y) co-ordinate is (0, -1)

Substitute x=-1 in the given equation y = x -1.

That is y= =-1 – 1 = -2

Therefore the (x, y) co-ordinate is (-2, -2)

Substitute x=-2 in the given equation y = x -1.

That is y= -2 – 1 = -3

Therefore the (x, y) co-ordinate is (-1, -3)

We can tabulate these points

X: -2 -1  0 1 2

Y: -3 -2 -1 0 1

Here the x and y values are correspondingly varies. So this function is namely known as step function.

The graph of the step function in math described as
Step function y=x-1


This is also known as Heaviside step functions in math.




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