Graphing Greatest-Integer Functions Algebraically and Explain?

Question

I know what Greatest-Integer is by definition and all; like [4.3]= 4, but how do i graph it by hand and using a graphing utility like my TI-83 calculator to graph it. And give me steps to complete it. Please and thank you!

Maybe I didn't word it correctly, but I would like someone to explain the graphing procedure by hand - while viewing the numbers.

Answer 1

Interesting!

Well, Megan, you can graph it by hand just like how every other relation is graphed...by writing up a table, plotting the points, and then connecting the dots. Just to let you know, it will be a step function and it will have pieces that are not connected. I guess once you will see on your calculator, you will have an idea.

First, there is a function called int( in TI-83 which returns the largest intger less than or equal to the argument. So int(4.3)=4 and int(-23.4)=-24. The easiest way to find it would be 2nd->Catalog->i and then scroll down to int( and then just press enter. Same way to graph it.

As for graphing it by hand, here is an example table:
(x,y)
(0,0)
(0.5,0)
(0.9,0)
(1,1)
(1.5,1)
(1.9,1)
(-1,-1)
(-0.9,-1)
(-0.5,-1)
(-0.1,-1)

and so on. It will look like a bunch of horizontal lines that will be one unit long. The detail (which the calculator will not show you) is that on the left end, it will be a close circle and on the right end, it will be an open circle, because at the right end, the function suddenly jumps up to the next step.

Once you graph it, you will see why we call it a step function.

Other functions to try on the TI-83 are ipart() and fpart().

ipart(value) just returns the integer part of the value AND IT IS NOT THE SAME AS int().

fpart(value) just return the fractional part (or the decimal part) of the value.

Graph all three of them and take a lot. It is pretty interesting.

Feel free to contact me if you need anymore help.

Answer 2

Greatest Integer Function

Answer 3

I doubt if the graphing calculator will do it since it is a discontinuos function. The graph will look like a staircase. The y axis remains at a single level between integer points on the x axis, and jumps an integer as the x value crosses an integer point.