anonymous
  • anonymous
g(t)=u(7t+sqrt3)
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
I have to plo\[g(t)=u(7t+\sqrt{3})\] and find at what points the function is discontinuous.
anonymous
  • anonymous
Example:\[f(t)=u(3t-7)\]\[3t-7=0\]\[3t=7\]\[t=\frac{ 3 }{ 7 }\]|dw:1440369141852:dw|
dan815
  • dan815
|dw:1440369231308:dw|

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anonymous
  • anonymous
Another Example: \[h(t)=u(-3t+7)\]\[-3t+7=0\]\[-3t=-7\]\[t=7/3\]|dw:1440369295368:dw|
dan815
  • dan815
http://prntscr.com/883u7t here is the defintion of a unit step function
dan815
  • dan815
that is where wherever the shift is taking place is where the discontinuity is
anonymous
  • anonymous
oh that makes more sense, so if I solve for 0, shouldn't I get when t=0?
anonymous
  • anonymous
and from the examples I was given, it seems that at those points is where the shift happens
dan815
  • dan815
|dw:1440369613756:dw|
dan815
  • dan815
i think you should really be thinking of what a function is and how transformations work
dan815
  • dan815
it just so happens that for this function solving for u(f(t)) where f(t)=0 is the discontinuty as u(0) is discont there
dan815
  • dan815
i say this because there might be some other ways to restrict this funtion that is not begin considered right now
anonymous
  • anonymous
So the shift doesn't always occur when it's at 0?
dan815
  • dan815
i dont know what you should really be thinking about is the bigger picture though that setting to 0 is more like a formula
anonymous
  • anonymous
or only if we follow |dw:1440370174580:dw|
dan815
  • dan815
you understand how function transformations work right like say g(t) and f(t) = a*g(b(t-c)) + d a,b,c,d are constants
dan815
  • dan815
f(t) is g(t) with vertical stretch of factor a, horizontal compression of b, shift to right of c and vertical shift of d
anonymous
  • anonymous
yes I understand all that
dan815
  • dan815
yeah thats all u need to know
dan815
  • dan815
and the definition of u(t) which u have
dan815
  • dan815
|dw:1440370382170:dw|
dan815
  • dan815
for example they can give u something like this, they you wouldnt worry about just setting bracket =0
dan815
  • dan815
there will be other places where the function is not defined like this
dan815
  • dan815
or suppose they started throwing t into radicals or having abs values in there and stuff like that
anonymous
  • anonymous
I don't think I'm ready for all that yet lol. I've only seen this for 1 class and I still have 1 doubt with the direction of the plot
anonymous
  • anonymous
Like for the second example, what made the plot switch directions?|dw:1440370886926:dw|

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