anonymous
  • anonymous
Greatest integer parent function: grt int(x). What is the function for grt int(x) shifted down one unit?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I 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
  • anonymous
@SolomonZelman Could you help me again?
SolomonZelman
  • SolomonZelman
|dw:1441668972134:dw|

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SolomonZelman
  • SolomonZelman
I am lagginging, i have to refresh. I will just say that to shift C unit down, subtract C from the entire function
anonymous
  • anonymous
Alright, thanks!
anonymous
  • anonymous
I'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
  • jim_thompson5910
https://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
  • SolomonZelman
The 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 x-values that are on the interval \(\bf [0,1)\), \((\)including 0, and not including 1\()\), then you get 0. When you plug in x-values 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 x-values 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
  • SolomonZelman
oh, in the third example, I wrote that it is equal to 14. I WAS WRONG it is 13.
SolomonZelman
  • SolomonZelman
because the greatest integer that is in 13.9 is 13. (Not 14, as I said)
SolomonZelman
  • SolomonZelman
If 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
  • SolomonZelman
((if you have learned about imaginary number i, thatis \(i=\sqrt{-1}\) ))
anonymous
  • anonymous
Awesome thanks.
SolomonZelman
  • SolomonZelman
yes, 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
  • SolomonZelman
So a parent greatest integer function \(\lfloor x\rfloor\) that is shifted one unit down, you can either right as: \(\large\color{black}{ \displaystyle f(x)=\lfloor x\rfloor-1 }\) Or, you can re-write it as: \(\large\color{black}{ \displaystyle f(x)=\lfloor x-1\rfloor }\)

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