Greatest Integer Function

[Zahra_Kaito]

Hi, I'm learning about quadratic functions and I came upon a lesson in my textbook about something called the "greatest integer function". I don't understand how it works, how to graph it, or how to know whether the point should be included as a solution or not, or why there are some points that aren't solutions. So...I was wondering if anyone here could explain it to me....

 

[lev888]

Hi, I'm learning about quadratic functions and I came upon a lesson in my textbook about something called the "greatest integer function". I don't understand how it works, how to graph it, or how to know whether the point should be included as a solution or not, or why there are some points that aren't solutions. So...I was wondering if anyone here could explain it to me....

Please post the page(s) you are referring to.

 

[Zahra_Kaito]

Well, this is the question, if that's what you want. Unfortunately, it's not very clear because I just took a screenshot and my laptop is very small:

 

[HallsofIvy]

The "greatest integer function", g(x), is the greatest integer less than or equal to x: g(8.9)= 8, g(23.2)= 23, g(-3.5)= -4, g(36/5)= 7, \(\displaystyle g(\sqrt{2})= 1\), etc.. Notice that its values are always integers so its graph consists of horizontal line segments. For any x in [0, 1), g(x)= 0 so the graph is the line segment from (0, 0) stopping just before (1, 0). For any x in [1, 2), g(x)= 1 so the graph is the line segment from(1,1) to just before (2, 1). The graph continues like that.

I don't know what that function has to do with quadratic functions.