Greatest Integer Function is a function that gives the greatest integer less than or equal to the number. We will round off the given number to the nearest integer that is less than or equal to the number itself. Clearly, the input variable x can take on any real value. However, the output will always be an integer.
Also, all integers will occur in the output set. Look at the following examples of the greatest integer function in the following table:. The greatest integer function graph is known as the step curve because of the step structure of the curve. Let us plot the greatest integer function graph. If x is a non-integer, then the value of x will be the integer just before x. The function has a constant value between any two integers.
As soon as the next integer comes, the function value jumps by one unit. These observations lead us to the following graph. From the graph above we can clearly see that inputs of the function can be any real number but the output will always be the integers. There are various properties related to greatest integrer function.
Some useful greatest integer function properties are listed below. The greatest integer part of a number is 0 if that number lies in the interval [0,1. Thus, to obtain the domain, this interval must be excluded from the set of real numbers.
Answer: x can take the values greater than or equal to 2 and less than 3. As we check the graph of the greatest integer function, we can see that it is jumping whenever it reaches an integer. Since the curve is discontinuous at integers, it is not differentiable at those points. Therefore at each integer, the greatest integer function is not differentiable. The greatest integer function is a function that gives the largest integer which is less than or equal to x.
The floor function or the greatest integer function is not differentiable at integers. The floor function has jumping values at integers, so its curve is known as the step curve. The curve of floor function is discontinuous at integers and hence not differentiable at integers. Learn about the math and science behind what students are into, from art to fashion and more. We are here to help with distance learning resources for schools and districts.
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