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korosh23
 one year ago
Calculus 12 Question!
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korosh23
 one year ago
Calculus 12 Question! Please wait for the attachment.

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korosh23
 one year ago
Best ResponseYou've already chosen the best response.0Please explain the whole solution. I don't understand it.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3where exactly are you stuck on the solution?

korosh23
 one year ago
Best ResponseYou've already chosen the best response.0I understand the slope and that the line passes those points. However, how to get the formula and the piecewise function. I don't understand. Could you please clarify it for me?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3they broke the function into 3 linear pieces each piece is really a full linear equation, but restricted on the domain

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3dw:1443244678300:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3dw:1443244692570:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3dw:1443244719667:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3dw:1443244752626:dw

korosh23
 one year ago
Best ResponseYou've already chosen the best response.0for the second lienear function f(x)= x +2 why 2 is not the yintercept?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3extend out the middle piece in both directions you'll see that piece cross 2 on the y axis

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3dw:1443244906871:dw

korosh23
 one year ago
Best ResponseYou've already chosen the best response.0one more thing, for the third function. why don't we say y=0 when x greater or equal to 2. Because at 2, y is 0

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3notice the \(\Large 1 < x \le 2\) as the restriction on the second piece if x = 2, then you use y = 2x to find y if we used \(\Large x \ge 2\) for the third piece, then that would mean x = 2 is defined for the third piece as well. Question is: which piece do we pick if x = 2? This ambiguity is a bad thing when it comes to functions. So that's why the restrictions are set up in a way to avoid letting x = 2 be defined for more than one piece

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3put another way, the fancy notation you see at the bottom really breaks down into this f(x) = x if 0 <= x <= 1 OR f(x) = 2x if 1 < x <= 2 OR f(x) = 0 if x > 2 each piece can't overlap another piece. Otherwise, we wouldn't have a function

korosh23
 one year ago
Best ResponseYou've already chosen the best response.0what do you mean by overlap?

korosh23
 one year ago
Best ResponseYou've already chosen the best response.0I believe connected does not mean overlapped

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3by overlap, I mean defined in multiple places

korosh23
 one year ago
Best ResponseYou've already chosen the best response.0Oh I see, and the last question. Can we say we have 3 formulas for the function?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0Is the formal way to put the solid point on the left function, or can you do whatever for the intervals

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3think of the 3 restrictions as number linesdw:1443245579767:dw

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0oh i didnt see tha tin the book , i was just wondering

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3now if we had x >= 2 for the third piece, then we have this overlap dw:1443245694279:dw

korosh23
 one year ago
Best ResponseYou've already chosen the best response.0Right, hollow ones mean the number itself does not include

korosh23
 one year ago
Best ResponseYou've already chosen the best response.0So if both are full. means overlapped becaue the numbers are present in two different equations.

korosh23
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 thank you my friend. I felt like I was in a classroom. lol

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0is it legal to reverse each solid  dot combo in between functions?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0i am guessing yes, since it describes the same thing, maybe

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3`is it legal to reverse each solid  dot combo in between functions?` I'm not sure what you mean. You mean use "solid" to mean "open/excluded endpoint" ? If so, then you're going against all of the conventional notation I've seen. That would be like making "up" be "down"

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0I think that step function wasopen  solid

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0typo corrected in next line, i just mean can you specify the intervals another way, for each interface between functions, can you choose arbitrarily which function will include the value

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.3oh, yeah you could say maybe 0 <= x < 1 1 <= x < 2 x >= 2 just as long as there is no overlap, you're fine

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0k, that is what i was trying to say, solidopen endpoint combo switch deal.. blahh

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0of course if that value is defined for both functions
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