4chan archive /sci/ (index)
2013-09-01 12:49 6002031 Anonymous (Untitled.png 869x380 491kB)
What am I doing wrong, /sci/? http://www.wolframalpha.com/input/? i=y%3D%E2%88%9A%281-%28x-2%29%5E2%2 9 I just don't get it.

4 min later 6002034 Anonymous
I have no clue what you're trying to do here.

16 min later 6002061 Anonymous (Untitled.png 338x245 20kB)
>>6002034 Here's the page on the textbook. I got every other question correct except this on and #39.

21 min later 6002071 Anonymous
>>6002034 I think he wants a function which has the curve he draw : http://www.wolframalpha.com/input/? i=y%3Dsqrt%281%2F4-%28x-5%2F2%29%5E 2%29 y=sqrt(1/4-(x-5/2)^2) (just use the equation of a circle)

23 min later 6002075 Anonymous
So this is #35? So you have y = \sqrt{1 - (x - 2)^{2}} . For x < 1 or x > 3, (x-2)2 > 1, and therefore 1 - (x-2)2 < 0, which means the square root is not real. For x = 1 and x = 3, (x-2)2 = 1, so y = 0. For x = 2, (x-2)2 = 0, so y = 1. You should calculate some intermediate values too, so you can get an idea of the shape of the curve. This really isn't a difficult problem.

24 min later 6002077 Anonymous
>>6002075 What the fuck, why doesn't 4chan support the squared symbol (unicode superscript 2)? It always used to.

25 min later 6002080 Anonymous
>>6002071 oops sorry, OP replied. So : 35 : y=g(x-2)=g(X) it just means that you will have the curve of g, but translated on the right "by 2" X=x-2 when x=2, X=0 >>6002075 is more complicated imo

27 min later 6002088 Anonymous
>>6002080 This presumes he has already calculated relevant values for g(x), though. My approach is only "more complicated" because it does this explicitly.

32 min later 6002098 Anonymous
>>6002077 yep, that's really boring, get used to ^ ... >>6002088 yes, sure. My way is more empiric, not always formally correct. I just think it's a good thing to have a genral idea of the changes to the curves made by f(ax) or f(x+a), f(1/x) but that's more useful for physics. I virtually delete my "complicated" and replace it by "more complete"

34 min later 6002102 Anonymous
>>6002098 >not always formally correct How could f(x-2) not be f(x) translated by 2 in the x-direction for any f and any complex x?

41 min later 6002114 Anonymous
I'm confused by this notation g(x) = sqrt^( 1 - x^2 ) f(x) = - g( x - 2 ) Does this mean that you immediately invert the signs of the function g(x) and then when calculating for a value 'x', i.e. x = 0, you minus 2 and actually calculate the function at x = -2

44 min later 6002120 Anonymous
>>6002031 I see where you got it wrong. You're thinking that (x-2)^2 is what would make it a parabola, but in reality, y=√(1-(x-2)^2) is a semicircle. The points are (-1,0),(0,1),(1,0). Just add two the x-axis to get your answer.

44 min later 6002122 Anonymous
>>6002102 I was speaking in general. We often use informal ways to draw curves in physics/signal processing which implies translations, rotations, dilatations, ...and combination of all these (sometimes in 2D but also in 3D). It's not always very acceptable for a mathematician, but we just want to "feel" the shape. But for X=x-2, no problem. >>6002114 I understand this as -[g(x-2)] If they want opposite of g, they should write (-g)(x-2)

53 min later 6002136 Anonymous
>>6002114 Just work from the inside out, and substitute precisely. If it helps, imagine every f(x) contained in parentheses, like [f(x)], so if you substitute anything for it, it will all be contained within those brackets. In this case: f(x) = -\Sqrt{1-x^{2}} - 2

1 hours later 6002156 Anonymous
>>6002136 f(x) = -\sqrt{1 - (x - 2)^{2}}

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