# Step Function Examples

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Step functions are the functions which take a particular value in a way that they jump from one constant value to another constant value. The graph of a step function looks like a staircase that increases upward or goes downward step-by-step. An example of a step function is the greatest integer function which is represented by the ‘[| |]’ symbol, and no matter what number is given inside the parentheses, only the integer which is lesser than or equal to the given number is considered as the answer!

Example 1: Find the greatest integer values of 4.2, 4.6 and 5.4.

Greatest integer means we have to only take the value of the greatest integer possible which is less than or equal to the given number.
This implies that the greatest integer less than or equal to 4.2 is ‘4’.
Therefore, [| 4.2 |] = 4
Similarly, [| 4.6 |] = 4
Also, [| 5.4 |] = 5

If when graphed, these values give a series of steps, and hence this kind of function is known as the step function!

Example 2: Find the greatest integer values of -2.1, -3.5 and -4.7.

Greatest integer means we have to only take the value of the greatest integer possible which is less than or equal to the given number.
This implies that the greatest integer less than or equal to -2.1 is ‘-3’.
Therefore, [| -2.1 |] = -3
Similarly, [| -3.5 |] = -4
Also, [| -4.7 |] = -5

If when graphed, these values give a series of steps, and hence this kind of function is known as the step function!