A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 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?

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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).

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @SolomonZelman Could you help me again?

  3. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1441668972134:dw|

  4. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I am lagginging, i have to refresh. I will just say that to shift C unit down, subtract C from the entire function

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Alright, thanks!

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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.

  7. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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"

  8. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    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: \(\large\color{red}{ \displaystyle f(x)=\lfloor x \rfloor}\) \(\large\color{royalblue }{ \displaystyle f(-2)=\lfloor -2 \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(-2)=-2}\) \(\large\color{green }{ \displaystyle f(4.5)=\lfloor 4.5 \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(-2)=4}\) \(\large\color{royalblue }{ \displaystyle f(13.9)=\lfloor 13.9 \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(13.9)=14}\) \(\large\color{green }{ \displaystyle f(0)=\lfloor 0 \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(0)=0}\) \(\large\color{royalblue }{ \displaystyle f(\pi)=\lfloor \pi \rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f(\pi)=3}\)

  9. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    oh, in the third example, I wrote that it is equal to 14. I WAS WRONG it is 13.

  10. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    because the greatest integer that is in 13.9 is 13. (Not 14, as I said)

  11. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    If you want to use something interesting, \(\large\color{brown }{ \displaystyle f({~}\rm i^i{~})=\lfloor {~}\rm i^i{~}\rfloor{~~~~~~}\Longrightarrow{~~~~~~}~f({~}\rm i^i{~})=0}\)

  12. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ((if you have learned about imaginary number i, thatis \(i=\sqrt{-1}\) ))

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Awesome thanks.

  14. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    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 \(\large \color{black}{a} \in \mathbb{Z} \)

  15. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    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: \(\large\color{black}{ \displaystyle f(x)=\lfloor x-1\rfloor }\)

  16. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.