Step Functions

In our day to day life we always experience step functions but we do not notice it mostly. If you have noticed about the calling rates of cell phone, as it is charged per minute. You generally pay a certain amount of money for the first minute. And as soon as we run over to the second minute you start paying. So let it be say, you have 1 min 2 sec. you pay the same. For example, if we understand by using an example, say a cell phone call rate is charged 40 cents per min. as soon as we go over 1 minute by 1 or 2 seconds we are charged double for the another minute as well that is another 40 cents been charged likewise we have to pay in all together 80 cents up to 2 minutes of a phone call. This was the brief example to understand the step function definition. When we graph it, it looks like steps. We notice on the graph, first minute of 0 to 1, 40 cents. And then as soon we hit 2, one second after 1 minute. We are charged 80 cents.

The step function graph looks like a staircase. What is the integer graph and how does it affects the function graph. F(x)=[(x)], it is a greatest integer function. It says nothing but give the greatest integer or less than or equal number in it. Let us say for example, [(3.7)] so as we know integers are all sort of whole numbers negative or positive. Here we are looking for the greatest or less than the or equal to 3.7. So 3.7 is not an integer by its own. So we have to go to the next smallest one, which is down to 3. So, [(3.7)] =3. Now what if the [(8)], here 8 is already an integer, so the greatest integer, less than or equal to 8 is 8. So [(8)]= 8.  Now what if the number is negative, say [(- 2.5)] here if we think about how we do it on a graph using step function on a number line. Step functions algebra 2 , we had studied that say like on a number line 3.7 is on the right side, we go down to 3. Then 10.2 on the number line , but we are going down to 10.but on number line – 2.5,we will not change the direction towards right side as we did in positive integers. But we end up going on -3.as we see on number line -3 is smaller than the -2.5.