Graphing Functions

[Borrowedhalo]

Hi all.

I have a sheet that says, "Graph each function" and the problems look like this - y=[[x+2]]

In the book it says the symbol [[x]] means the greatest integer less than or equal to x. For example, [[3.25]] = 3 and [[-4.6]] = 5.

Ok, so it looks like sort of rounding. But I don't know how to apply that to what I'm supposed to do.

FYI, in case you haven't read my previous posts, I am a mom trying to help an LD son. Unfortunately, that means I do not have the advantage of listening during class. I could call the teacher; but on a holiday weekend that just seems tacky!

Thanks everyone!

Kristine

 

[HallsofIvy]

Hi all.

I have a sheet that says, "Graph each function" and the problems look like this - y=[[x+2]]

In the book it says the symbol [[x]] means the greatest integer less than or equal to x. For example, [[3.25]] = 3 and [[-4.6]] = 5.

Okay, for x between 0 and 1, x+ 2 is between 2 and 3 and so [[x+2]]= 2 for every such x. Now that means that the graph is a horizontal straight line at y= 2 for x between 0 and 1. (If x= 0, [[x+ 2]]= 2 while if x= 1, [[x+2]]= 3 NOT 2. A standard way of showing that one endpoint of the horizontal line and the other isn't is to draw an "open dot", o, at the right end at (1, 2) which is NOT part of the graph and a closed dot, with the center drawn in, at the left end at (0, 2). Now do the same kind of thing for x from 1 to 2. x+ 2 is between 3 and 4 so [[x+ 2]]= 3. The graph is a horizontal line at height y= 3. At x= 2, x+ 2 jumps to 4 and the graph jumps to y= 4. That is, your graph is a series of horizontal lines.

Ok, so it looks like sort of rounding. But I don't know how to apply that to what I'm supposed to do.

FYI, in case you haven't read my previous posts, I am a mom trying to help an LD son. Unfortunately, that means I do not have the advantage of listening during class. I could call the teacher; but on a holiday weekend that just seems tacky!

Thanks everyone!

Kristine

 

[JeffM]

Hi all.

I have a sheet that says, "Graph each function" and the problems look like this - y=[[x+2]]

In the book it says the symbol [[x]] means the greatest integer less than or equal to x. For example, [[3.25]] = 3 and [[-4.6]] = 5. Are you sure that it does not say - 5?

Ok, so it looks like sort of rounding. Technically, it is often called truncating. But I don't know how to apply that to what I'm supposed to do.

FYI, in case you haven't read my previous posts, I am a mom trying to help an LD son. Unfortunately, that means I do not have the advantage of listening during class. I could call the teacher; but on a holiday weekend that just seems tacky!

Thanks everyone!

Kristine

I remember being confused about function notation when I was first studying algebra, but I can no longer remember why.

\(\displaystyle - y = [[x + 2]] \implies y = -[[x + 2]] \implies f(x) = - [[x + 2]].\)

What that means is that f(1) is equal to whatever you get when you compute -[[1 + 2]]. f(2) is equal to whatever you get
when you compute -[[2 + 2]], and so on. A function is a machine that spits out a numeric answer according to a rule when you put a number into it. (This is an over-simplification, but it is a great starting place.) If you click on the word "function" in blue in the second sentence of YOUR original post, you will get a brief tutorial on functions.

Now this problem is a little tricky because [[4.6]] = 4, but [[-4.6]] = - 5. Do you see why?

So what is -[[4.6]] and what is -[[-4.6]]?

 

[HallsofIvy]

JeffM, you are interpreting the "-" in "the problems look like this - y=[[x+2]]" as a "negative". I am interpreting it as just a "dash" and that the actual function is "y= [[x+2]]" (standard notation \(\displaystyle y= \lfloor x+ 2\rfloor\)).

BorrowedHalo, you will need to tell us which is correct.

 

[JeffM]

JeffM, you are interpreting the "-" in "the problems look like this - y=[[x+2]]" as a "negative". I am interpreting it as just a "dash" and that the actual function is "y= [[x+2]]" (standard notation \(\displaystyle y= \lfloor x+ 2\rfloor\)).

BorrowedHalo, you will need to tell us which is correct.

You are right, Halls. I made an assumption. I should have asked.