Greatest Integer Function help

In summary, the problem is about a plumber who charges $80 for arrival and an additional $25 per hour. The attempted solution of y=28[(x+1)]+80 is incorrect as it would result in charging 2 hours for 1 hour of work. The correct solution involves replacing (x+1) with another expression and can be checked using the same method. The conversation does not mention anything about the greatest integer function.
  • #1
Kino
2
0
Greatest Integer Function.. help!

Homework Statement


Well this is the problem a plomer charges 80 bucks ones he arrives at your home and charges and extra 25 per hour.. Give the equation,,
Kind of i don't get it is for extra credit but still i don't like it when i don't know how to do it

2. The attempt at a solution
i put these but i think is wrong..
y=28[(x+1)]+80
But if i put 1hour.. plus 1 gives 2 hours so he would be chargin 2 hours just for working one..
Nice deal! hahaha But still i don't think this is it
 
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  • #2
Welcome to PF!

Hi Kino! Welcome to PF! :smile:
Kino said:
… a plomer charges 80 bucks ones he arrives at your home and charges and extra 25 per hour..
…
y=28[(x+1)]+80

Well, basically it's right (except for the "28" of course :wink:) …

you just need to replace (x+1) by something else …

then you can check that it's right in exactly the same way that you checked that (x+1) was wrong. :smile:

(btw, what did this have to do with "greatest integer"? :confused:)
 
  • #3


I meant the parentesis are the integers signs but i didnt now how to put them...
But today i may get the answer so i'll publish it
 

1. What is the greatest integer function?

The greatest integer function, denoted by ⌊x⌋ or sometimes [x], is a mathematical function that rounds any real number down to the nearest integer. This means that any decimal or fractional part of the number is dropped, and only the integer part remains.

2. How do you graph the greatest integer function?

The graph of the greatest integer function is a series of horizontal line segments, with each segment representing a different integer value. For example, the segment between x = 0 and x = 1 would have a height of 0, since the greatest integer less than or equal to 1 is 0. The segment between x = 1 and x = 2 would have a height of 1, and so on.

3. What is the domain and range of the greatest integer function?

The domain of the greatest integer function is all real numbers, since any real number can be rounded down to an integer. The range, however, is only the set of integers, since the function always outputs an integer value.

4. How is the greatest integer function used in real-life situations?

The greatest integer function is commonly used in computer programming, particularly for truncating or rounding down decimal numbers. It can also be used in finance to round down prices or interest rates. In addition, it can be used in statistics to represent discrete data.

5. How does the greatest integer function differ from the ceiling function?

The greatest integer function rounds a number down to the nearest integer, while the ceiling function rounds a number up to the nearest integer. In other words, the ceiling function always outputs the smallest integer that is greater than or equal to the input, while the greatest integer function always outputs the largest integer that is less than or equal to the input.

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