A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Greatest integer parent function: grt int(x). What is the function for grt int(x) shifted down one unit?
anonymous
 one year ago
Greatest integer parent function: grt int(x). What is the function for grt int(x) shifted down one unit?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I tried graphing grt int(x) + 1 (in calc: floor(x) + 1) but it looks like the graph for shifting horizontally (grt int (x + 1).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@SolomonZelman Could you help me again?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3dw:1441668972134:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I am lagginging, i have to refresh. I will just say that to shift C unit down, subtract C from the entire function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm an idiot, I just realized since it's steps it just elongates each step a bit, nevermind, that's why it looks like the other graph. Thanks for the help.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0https://www.desmos.com/calculator/6odyay0pdt notice how the red parent function `floor(x)` gets shifted down 1 unit to get to `floor(x)1` the "floor" function is another way to state the "greatest integer function"

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3The greatest integer (parent) function, also known as the floor function {of x}, is often denoted by: \(\large\color{blue}{ \displaystyle f(x)=\lfloor x \rfloor}\) Or basically, that when you plug in xvalues that are on the interval \(\bf [0,1)\), \((\)including 0, and not including 1\()\), then you get 0. When you plug in xvalues that are on the interval \(\bf [1,2)\), \((\)including 1, and not including 2\()\), then you get 1. And so it is true that when you plug in xvalues from some {and including an} integer \(\bf C\), and till {but, not including \({\bf C}+1\)}, then you get \(\bf C\).  here, are some examples: In a case where: \(\large\color{red}{ \displaystyle f(x)=\lfloor x \rfloor}\) \(\large\color{royalblue }{ \displaystyle f(2)=\lfloor 2 \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(2)=2}\) \(\large\color{green }{ \displaystyle f(4.5)=\lfloor 4.5 \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(2)=4}\) \(\large\color{royalblue }{ \displaystyle f(13.9)=\lfloor 13.9 \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(13.9)=14}\) \(\large\color{green }{ \displaystyle f(0)=\lfloor 0 \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(0)=0}\) \(\large\color{royalblue }{ \displaystyle f(\pi)=\lfloor \pi \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(\pi)=3}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3oh, in the third example, I wrote that it is equal to 14. I WAS WRONG it is 13.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3because the greatest integer that is in 13.9 is 13. (Not 14, as I said)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3If you want to use something interesting, \(\large\color{brown }{ \displaystyle f({~}\rm i^i{~})=\lfloor {~}\rm i^i{~}\rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f({~}\rm i^i{~})=0}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3((if you have learned about imaginary number i, thatis \(i=\sqrt{1}\) ))

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3yes, just in case, verifying, that if you want to shift it C units up/down, right/left then it follows regular rules (And just like by a line, shift right =shift down, and shift left = shift up) Like I mean that: \(\large\color{black}{ \displaystyle f(x)=\lfloor x+a\rfloor\ }\) is same as \(\large\color{black}{ \displaystyle f(x)=\lfloor x\rfloor\ +a}\) where \(\large \color{black}{a} \in \mathbb{Z} \)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3So a parent greatest integer function \(\lfloor x\rfloor\) that is shifted one unit down, you can either right as: \(\large\color{black}{ \displaystyle f(x)=\lfloor x\rfloor1 }\) Or, you can rewrite it as: \(\large\color{black}{ \displaystyle f(x)=\lfloor x1\rfloor }\)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.