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bbolman
Newbie
Joined: 29 Nov 2007
Posts: 7
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 Posted: 03 Dec 2007 06:46:23 pm Post subject: |
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I'm trying to figure out how one would graph a Piecewise Function or a Greatest Integer Function on a calculator (I've got an 84 SE).
For reference, an example of a Piecewise Function would be:
f(x) = 1/2x+3/2, if x < 1
-x+3, IF x > 1
(all of that is in a bracket)
And a Greatest Integer function would be:
f(x) = [[x]]
( f(1)= 1 and f(0.6)=1 )
Last edited by Guest on 03 Dec 2007 06:59:30 pm; edited 1 time in total |
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JoostinOnline
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Joined: 22 Aug 2007
Posts: 559
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| Posted: 03 Dec 2007 07:01:16 pm Post subject: |
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Do this:
Y1=(X<1)(.5X+1.5)+(X>1)(-X+3) |
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bbolman
Newbie
Joined: 29 Nov 2007
Posts: 7
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| Posted: 03 Dec 2007 07:13:44 pm Post subject: |
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Brilliant. thanks. I can't believe I didn't think of that...
Figured out the second. it's y1 = int(x)
Last edited by Guest on 03 Dec 2007 07:27:17 pm; edited 1 time in total |
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JoostinOnline
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Joined: 22 Aug 2007
Posts: 559
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| Posted: 03 Dec 2007 07:18:12 pm Post subject: |
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No problem, and welcome to UTI  |
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DarkerLine
ceci n'est pas une |
Super Elite (Last Title)
Joined: 04 Nov 2003
Posts: 8328
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| Posted: 03 Dec 2007 07:25:41 pm Post subject: |
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| As for the greatest integer function, it's implemented with int(, but the examples you give seem to indicate you're thinking of the least integer function, which you can calculate with -int(-X). |
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bbolman
Newbie
Joined: 29 Nov 2007
Posts: 7
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| Posted: 03 Dec 2007 08:12:38 pm Post subject: |
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Thanks to both of you. I figured out the greatest integer bit right before your post.
DarkerLine, wouldn't my example be an example of the greatest integer function? We just learned this today and my teacher gave 0 explanation, so I could be wrong.
Last edited by Guest on 03 Dec 2007 08:15:54 pm; edited 1 time in total |
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DarkerLine
ceci n'est pas une |
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Joined: 04 Nov 2003
Posts: 8328
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| Posted: 03 Dec 2007 09:25:21 pm Post subject: |
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The greatest integer function is defined as the greatest integer (duh) which is less than or equal to x. So f(0.6) is 0.
However, the "least integer" function is defined as the least integer which is greater than or equal to x. Here, f(0.6) is 1.
Naturally, this is quite confusing because "greatest integer" returns a smaller result than "least integer." So most people refer to this as "ceiling" and "floor" - floor rounds down to an integer, and ceiling rounds up to an integer.
While the TI-89 has floor() and ceiling() commands, the TI-83+ series calculators have the int() command, so you use int(X) for floor(X) and -int(-X) for ceiling(X). Can you see why -int(-X) works?
Last edited by Guest on 03 Dec 2007 09:26:35 pm; edited 1 time in total |
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Pseudoprogrammer
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Joined: 12 Dec 2006
Posts: 121
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| Posted: 03 Dec 2007 09:47:01 pm Post subject: |
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Quote: Code: Y1=(X<1)(.5X+1.5)+(X>1)(-X+3)
Can be optimized, the -X+3 can be 3-X right? |
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JoostinOnline
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Joined: 22 Aug 2007
Posts: 559
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| Posted: 03 Dec 2007 09:53:23 pm Post subject: |
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| Yes, but I didn't want to change the example that he gave around. Also, since this is only about a graph and not programming, I didn't think that saving a byte mattered. |
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thornahawk
μολών λαβέ
Active Member
Joined: 27 Mar 2005
Posts: 569
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| Posted: 03 Dec 2007 10:19:17 pm Post subject: |
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To add: the nearest integer function nint(x) can be done on the TI 83/84/+ as either round(X,0) or int(.5+X).
The Iverson bracket notation, methinks, is more useful, both on the calculator and mathematically, than the "bracketed" piecewise notation.
I mean, it's easier to see that 1−(X>0) and (X≤0) refer to the same thing. :)
thornahawk
Last edited by Guest on 03 Dec 2007 10:20:43 pm; edited 1 time in total |
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bbolman
Newbie
Joined: 29 Nov 2007
Posts: 7
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| Posted: 03 Dec 2007 11:46:06 pm Post subject: |
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DarkerLine wrote: The greatest integer function is defined as the greatest integer (duh) which is less than or equal to x. So f(0.6) is 0.
However, the "least integer" function is defined as the least integer which is greater than or equal to x. Here, f(0.6) is 1.
Naturally, this is quite confusing because "greatest integer" returns a smaller result than "least integer." So most people refer to this as "ceiling" and "floor" - floor rounds down to an integer, and ceiling rounds up to an integer.
While the TI-89 has floor() and ceiling() commands, the TI-83+ series calculators have the int() command, so you use int(X) for floor(X) and -int(-X) for ceiling(X). Can you see why -int(-X) works?
[post="116826"]<{POST_SNAPBACK}>[/post]
Definitely counterintuitive, but I get it now. Much appreciated.
I was puzzling out why the -int(-x) works. Does the negative change the operator and what it's looking for? so, it instead looks for the opposite of the greatest integer (which would be the least), that is greater than (flipped from less than) X? |
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thornahawk
μολών λαβέ
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Joined: 27 Mar 2005
Posts: 569
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| Posted: 04 Dec 2007 07:57:30 am Post subject: |
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Quote: I was puzzling out why the -int(-x) works. Does the negative change the operator and what it's looking for? so, it instead looks for the opposite of the greatest integer (which would be the least), that is greater than (flipped from less than) X?
See these examples, and your question might be answered:
int(2.2) == 2 (because 2≤2.2<3)
while
int(-2.2) == -3 (because -3≤-2.2<2)
and therefore
-int(-2.2) == 3 (because 3≥2.2>2)
Remember that negating both sides of an inequality changes the "sense" of the inequality sign, e.g. negating both sides of a greater than relation changes ">" into "<". :)
thornahawk |
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