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Posted: February 2, 2009 08:52 pm  | |||||||
     IRC Nickname: Sum41xx Group: Emeritus Posts: 630 Member No.: 102 Joined: January 3, 2008 Total Events Attended: 0    | Alright. So I'm taking advanced functions and I haven't done math for pretty much 2 years now and I need some help reviewing. So pretty much I know that there's 7 basic functions: Linear Quadratic Rational Square Root Absolute Value Exponential Sinusoidal Help that I need is remember how those last 5 work. I remember them slightly but yeah.... So I need help with the Rational, Square Root, Absolute Value, Exponential, and Sinusoidal. So can you guys throw me the formulas for those and maybe some examples?  Thanks. PS please reply within the next day or two because my course moves quick and chances are that we'll be passed this part in the next class or two. --------------------   Proud WG member since December 2003 | ||||||
Posted: February 2, 2009 09:42 pm | |||||||
 IRC Nickname: Wayne|Eregion2 Group: Emeritus Posts: 3087 Member No.: 156 Joined: January 25, 2008 Total Events Attended: 8 | A rational function is any function that can be explained as a ratio of two polynomial functions [i.e. P(x) divided by Q(x)]. Someone check me on this, but I'm fairly sure that F(x) itself is a rational function, since you can divide it by 1. In comparison, irrational functions cannot be represented as the ratio of two polynomial functions [i.e. non-repeating, non-ending]. F(x) = (x - 1) / (x - 4) <-- Rational. F(x) = (x - 1) / π <-- Irrational, since pi is an irrational constant. Square root functions are functions of square roots. They have a positive domain so x cannot equal a negative number (unless, for example, you have the square root of x to a positive power, which would make a negative value positive anyway). Square root functions can be rational or irrational, since not all square root values can be defined as the ratio of two distinct numbers. F(x) = √x F(4) = √4 F(4) = 2 <-- Because you square 2 to get 4, so the square root of 4 is 2. F(x) = √x(to the power of 4) F(-3) = √-3(to the power of 4) F(-3) = √81 F(-3) = 9 <-- Multiplying a negative number to a positive exponent works. You shouldn't have the square root of a value to a positive exponent though anyway, since they'd cancel each other out. Absolute value functions are pretty simple. If you've got F(x) = |x| it just means that whatever you get between the two "|s" automatically becomes the absolute value, or positive value, when you're done working it out. F(x) = |x - 4| F(3) = |3 - 4| F(3) = |-1| F(3) = 1 <-- The absolute value of -1. Exponential functions occur when a value is multiplied by a power including a variable. Logarithms are so much fun.  Sinusoidal functions I'd never heard of by that name, but it looks like they're all functions involving trigonometric values (sine, cosine, etc) that create waves or wavelengths (so I think that rules out the tangent and cotangent, which have limits instead of continuous domains).That good? Not sure how well I explained it all tbh.  I haven't done math for several months before calculus class this semester, so this was a good review for me as well. What I'd like to know though, is what they call a function with more than one of these values. Like, the absolute value of a square root function to the power of five all divided by the cosine of x. Who wins? --------------------  | ||||||
Posted: February 2, 2009 10:12 pm | |||||||
 IRC Nickname: [Narita] Group: Guest Posts: 695 Member No.: 1378 Joined: October 15, 2008 Total Events Attended: 34 | erigons got it but its MATHS not math we created the english language so yer! -------------------- | ||||||
Posted: February 2, 2009 10:16 pm | |||||||
| IRC Nickname: Wayne|Eregion2 Group: Emeritus Posts: 3087 Member No.: 156 Joined: January 25, 2008 Total Events Attended: 8 | Yeah, but you guys never did get anything right on the first try.  *jibe* We're just improvin' it. -------------------- | ||||||
Posted: February 2, 2009 10:16 pm | |||||||
| IRC Nickname: Mojohaza1 Group: Council Posts: 495 Member No.: 1574 Joined: December 22, 2008 Total Events Attended: 33 |
what he said -------------------- | ||||||
Posted: February 3, 2009 12:06 am | |||||||
| IRC Nickname: Mangomaniac2 Group: Emeritus Posts: 536 Member No.: 70 Joined: December 31, 2007 Total Events Attended: 63 |
Sounds good. Eregion did a nice job explaining it all. An example of an exponential function would be 2^x (Two raised to the power of x), or some constant raised to a variable. Not sure if log functions are considered exponential, but they might be. And I've rarely heard the name sinusoidal functions, but at first glance, I also thought they were sine and cosine functions. Hope that helps, although Eregion did everything first  --------------------  | ||||||
Posted: February 3, 2009 12:34 am | |||||||
 IRC Nickname: Matt|Georgio9 Group: Emeritus Posts: 706 Member No.: 94 Joined: January 3, 2008 Total Events Attended: 0 | Sinusoidal functions are like my life right now lol. So basically a sinusoidal function is a periodic function, periodic meaning that it repeats after a given period of time or with respect to whatever unit you are referring to. So yes, Cosine and Sine functions are sinusoidal in nature.  The difference between the Sine function and the Cosine function is that Cosine actually leads the Sine function by Pi/2 radians or 90 degrees. (2Pi radians = 360 degrees) The equation to model a sinusoidal wave can be as such: y(t) = A cos( wt + B ) + C Where y(t) is the amplitude of the wave at a specific period of time, t. A is the maximum positive or negative value from the offset value, C (generally C is equal to 0). The value that determines how fast the function cycles through is w. The greater w is, the higher the frequency of the period is ( frequency is the inverse of the time it takes for the function to complete one period. ). w is generally multiplied by 2Pi so that it is converted into the unit of radians per second. B is a constant generally and it offsets the phase of the function. It is typically in radians or degrees. I think that should do it. I don't think you need to know leading and lagging functions or any of Euler's theorems on complex numbers... --------------------   | ||||||
Posted: February 3, 2009 03:37 am | |||||||
| IRC Nickname: Sum41xx Group: Emeritus Posts: 630 Member No.: 102 Joined: January 3, 2008 Total Events Attended: 0 | Wow thanks a million every1! Especially Eregion u killed it !  U guys helped out a lot, u have no idea  -------------------- Proud WG member since December 2003 | ||||||
Posted: February 3, 2009 09:19 am | |||||||
 IRC Nickname: Jesseh Group: Guest Posts: 2670 Member No.: 297 Joined: March 8, 2008 Total Events Attended: 222 | Wow cool, maths i've never seen before! --------------------   17/6/08--> 12/9/08--> 29/11/08--> 5/1/09--> 2/3/09(Left)--> 19/7/09(Rejoin)--> 2/8/09
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Posted: February 3, 2009 11:13 am | |||||||
 IRC Nickname: Maths Group: Ex-Member Posts: 1855 Member No.: 54 Joined: December 31, 2007 Total Events Attended: 286 | Hai I maffs  --------------------  "Journeys are what brings us happiness, Not the destination." ~ Two time ex-raid leader of wg ~  | ||||||
Posted: February 3, 2009 11:52 pm | |||||||
| IRC Nickname: Matt|Georgio9 Group: Emeritus Posts: 706 Member No.: 94 Joined: January 3, 2008 Total Events Attended: 0 |
ur ugly complex math that I'm totally killing right now. Just remember e^i*Pi = (-1) Complex plane proof k? -------------------- | ||||||
Posted: February 4, 2009 06:49 pm | |||||||
| IRC Nickname: Wayne|Eregion2 Group: Emeritus Posts: 3087 Member No.: 156 Joined: January 25, 2008 Total Events Attended: 8 | Why won't my calculator give me an answer for πLn -1.  -------------------- | ||||||
Posted: February 4, 2009 08:07 pm | |||||||
| IRC Nickname: Matt|Georgio9 Group: Emeritus Posts: 706 Member No.: 94 Joined: January 3, 2008 Total Events Attended: 0 |
square root of -1 on a calculator... you're calculator just failz. The only thing my casio can't do is matrices in complex numbers. casio fx-991ms is amazing for not being a graphing calculator. Square root of -1 is j or -j. i as an imaginary number is for the weak. Us electrical engineers use j. -------------------- | ||||||
Posted: February 4, 2009 09:45 pm | |||||||
| IRC Nickname: Wayne|Eregion2 Group: Emeritus Posts: 3087 Member No.: 156 Joined: January 25, 2008 Total Events Attended: 8 |  -------------------- | ||||||
Posted: February 5, 2009 01:16 am | |||||||
| IRC Nickname: Sum41xx Group: Emeritus Posts: 630 Member No.: 102 Joined: January 3, 2008 Total Events Attended: 0 |
I gots the TI-84 Plus -------------------- Proud WG member since December 2003 | ||||||
Posted: February 5, 2009 04:00 am | |||||||
| IRC Nickname: Matt|Georgio9 Group: Emeritus Posts: 706 Member No.: 94 Joined: January 3, 2008 Total Events Attended: 0 |
Cant use those on midterms and exams so I don't bother with one. Besides I have MATLAB and Maple 11 on my laptop. Both programs beat the shit out of any graphing calculator any day  -------------------- | ||||||
Posted: February 5, 2009 04:47 am | |||||||
| IRC Nickname: Wayne|Eregion2 Group: Emeritus Posts: 3087 Member No.: 156 Joined: January 25, 2008 Total Events Attended: 8 | What's a TI-84 got that a TI-83 hasn't got.  *glowers at the calculator* -------------------- | ||||||
Posted: February 5, 2009 11:59 pm | |||||||
| IRC Nickname: Sum41xx Group: Emeritus Posts: 630 Member No.: 102 Joined: January 3, 2008 Total Events Attended: 0 |
Well for one u can play video games on it like super mario other than that i dont know -------------------- Proud WG member since December 2003 | ||||||
Posted: February 6, 2009 12:00 am | |||||||
| IRC Nickname: Wayne|Eregion2 Group: Emeritus Posts: 3087 Member No.: 156 Joined: January 25, 2008 Total Events Attended: 8 | Maybe I've just got my settings messed or w/e.  -------------------- | ||||||
Posted: February 6, 2009 12:02 am | |||||||
| IRC Nickname: Mangomaniac2 Group: Emeritus Posts: 536 Member No.: 70 Joined: December 31, 2007 Total Events Attended: 63 |
The cool look. I have a TI-84 silver, and it wins  They've come out with two even newer ones, the TI-89 and TI-nSpire (sp?). The TI-89 is the next version up, and knows derivates, integrals, summations, and a ton more  TI-nSpire is even more advanced, and you can type word documents on it I think -------------------- | ||||||
Posted: February 6, 2009 04:21 pm | |||||||
 IRC Nickname: Samurai-JM Group: Emeritus Posts: 3204 Member No.: 117 Joined: January 11, 2008 Total Events Attended: 8 | My calculator wins. It's called a laptop. I can play Crysis on it with max settings. -------------------- -=}¤- Vi Veri Veniversum Vivus Vici -¤{=-  W I N N I N G | ||||||
Posted: February 6, 2009 05:06 pm | |||||||
 IRC Nickname: Zlat Group: Clan Friend Posts: 2781 Member No.: 9 Joined: December 29, 2007 Total Events Attended: 60 | holy shit. im still on the 5+5 level. --------------------   | ||||||
Posted: February 13, 2009 07:13 pm | |||||||
| IRC Nickname: Group: Clan Friend Posts: 31 Member No.: 1716 Joined: February 13, 2009 Total Events Attended: 0 | So this is a week old topic but yeah... Just though I'd mention that "Sinusoidal" functions (namely those dominated by a sin function) are really just exponentials, namely, a sum of exponentials, as can be seen doing a taylor expansion. Most importantly, is Euler's (pronounced Oiler) formula, which states that e^(xi), where x is some angle, can be expressed as cos(x) + isin(x). If you know how to work with complex numbers this makes trig identites MUCH easier. -------------------- | ||||||
Posted: February 14, 2009 05:13 pm | |||||||
| IRC Nickname: Wayne|Eregion2 Group: Emeritus Posts: 3087 Member No.: 156 Joined: January 25, 2008 Total Events Attended: 8 |
That. Is. Awesome. -------------------- | ||||||
Math, Advanced Functions :D