Looking for something else?

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

## More answers

Looking for something else?

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

- anonymous

Greatest integer parent function: grt int(x). What is the function for grt int(x) shifted down one unit?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

Get your **free** account and access **expert** answers to this and **thousands** of other questions

- anonymous

- katieb

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- 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

@SolomonZelman Could you help me again?

- SolomonZelman

|dw:1441668972134:dw|

Looking for something else?

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

- 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

Alright, thanks!

- 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

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

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

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

- SolomonZelman

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

- 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

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

- anonymous

Awesome thanks.

- 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

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

Looking for something else?

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