# Thread: Graphing using largest integer function

1. ## Graphing using largest integer function

The question is:
"The symbol [x] denotes the largest integer which is less than or equal to x. For example [2.4] = 2, [3] = 3, [-1.2] = -2. Draw the graph of: (see attached)

Any help would be greatly appreciated, I am really stumped as to how it would look.

2. ## Re: Graphing using largest integer function

on the interval $[0,1)$, $y_0 = 0 + \sqrt{x - 0} = \sqrt{x}$

on the interval $[1,2)$, $y_1 = 1 + \sqrt{x - 1}$, the graph of $y_0$ shifted right one unit and up one unit

on the interval $[2,3)$, $y = 2 + \sqrt{x - 2} = 1 + \left[1 + \sqrt{(x-1)-1}\right]$, the graph of $y_1$ shifted right one unit and up one unit

the pattern repeats on subsequent (and prior) intervals ...

3. ## Re: Graphing using largest integer function

Originally Posted by thebestrose828
The question is:
"The symbol [x] denotes the largest integer which is less than or equal to x. For example [2.4] = 2, [3] = 3, [-1.2] = -2. Draw the graph of: (see attached)
Any help would be greatly appreciated, I am really stumped as to how it would look.
Here is the plot.
In most cases, in modern mathematics the floor function is substituted for the greatest integer fumction.