anonymous one year ago g(t)=u(7t+sqrt3)

1. anonymous

I have to plo$g(t)=u(7t+\sqrt{3})$ and find at what points the function is discontinuous.

2. anonymous

Example:$f(t)=u(3t-7)$$3t-7=0$$3t=7$$t=\frac{ 3 }{ 7 }$|dw:1440369141852:dw|

3. dan815

|dw:1440369231308:dw|

4. anonymous

Another Example: $h(t)=u(-3t+7)$$-3t+7=0$$-3t=-7$$t=7/3$|dw:1440369295368:dw|

5. dan815

http://prntscr.com/883u7t here is the defintion of a unit step function

6. dan815

that is where wherever the shift is taking place is where the discontinuity is

7. anonymous

oh that makes more sense, so if I solve for 0, shouldn't I get when t=0?

8. anonymous

and from the examples I was given, it seems that at those points is where the shift happens

9. dan815

|dw:1440369613756:dw|

10. dan815

i think you should really be thinking of what a function is and how transformations work

11. 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

12. dan815

i say this because there might be some other ways to restrict this funtion that is not begin considered right now

13. anonymous

So the shift doesn't always occur when it's at 0?

14. 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

15. anonymous

or only if we follow |dw:1440370174580:dw|

16. 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

17. 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

18. anonymous

yes I understand all that

19. dan815

yeah thats all u need to know

20. dan815

and the definition of u(t) which u have

21. dan815

|dw:1440370382170:dw|

22. dan815

for example they can give u something like this, they you wouldnt worry about just setting bracket =0

23. dan815

there will be other places where the function is not defined like this

24. dan815

or suppose they started throwing t into radicals or having abs values in there and stuff like that

25. 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

26. anonymous

Like for the second example, what made the plot switch directions?|dw:1440370886926:dw|