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## anonymous one year ago Tristen and gorge are stuck simplifying radical expressions. Tristren has to simplify . William has to simplify . Using full sentences, describe how to fully simplify Vanessa and William's expressions. Describe if Tristena dn George started with equivalent expressions or if they started with expressions that are not equal?

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1. anonymous

they are the same equations...

2. anonymous

@Michele_Laino

3. Michele_Laino

Vanessa will simplify as below: ${x^{4/3 - 5/6}} = {x^{3/6}} = {x^{1/2}} = \sqrt x$

4. Michele_Laino

William will simplify as below: $\sqrt[{16}]{{{x^{1 + 3 + 4}}}} = \sqrt[{16}]{{{x^8}}} = {x^{8/16}} = {x^{1/2}} = \sqrt x$

5. anonymous

for vanessesa isn't it saying to divide?

6. Michele_Laino

yes! infact I have computed the difference between exponents

7. anonymous

okay:)

8. anonymous

Can you help with this one?

9. Michele_Laino

ok!

10. Michele_Laino

let's suppose that the graph of f(x) is: |dw:1437512461162:dw|

11. Michele_Laino

namely f(0)=5

12. anonymous

Yes

13. Michele_Laino

here is the graph of f(x)+2: |dw:1437512550200:dw|

14. anonymous

I see

15. Michele_Laino

here is the graph of -2*f(x): |dw:1437512657609:dw|

16. Michele_Laino

namely if g(x)=-2*f(x), then: g(0)=-10

17. anonymous

@Michele_Laino so where would it be increasing

18. Michele_Laino

the y-intercept for f(x)+2 is greater than the y-intercept of f(x)

19. Michele_Laino

whereas the y-intercept of g(x)=-2*f(x), is less than the y-intercept of f(x), if the y-intercept of f(x) is positive, and viceversa if the y-intercept of f(x) is negative

20. anonymous

How did you get that answer?

21. anonymous

isn't it -1/2 times f(x)

22. Michele_Laino

for example if the y-intercept of f(x) is 5, as in my drawing, then the y-intercept of -2*f(x), is -2*5=-10<5

23. Michele_Laino

oh sorry, I have made an error, I have considered the function -2*f(x) I have to consider the function -0.5 * f(x). here is the right drawing: |dw:1437513335915:dw|

24. Michele_Laino

the y-intercept of g(x)=-0.5*f(x), is less than the y-intercept of f(x), if the y-intercept of f(x) is positive, and viceversa if the y-intercept of f(x) is negative

25. Michele_Laino

for example if the y-intercept of f(x) is 5, as in my drawing, then the y-intercept of -0.5*f(x), is -2.5 <5

26. anonymous

what about where the graphs are increasing/decreasing. I mean the points

27. Michele_Laino

whereas if the y-intercept of f(x) is -7, then the y-intercept of -0.5*f(x), is: -0.5*(-7)=3.5 > -7

28. Michele_Laino

as you can see from m,y last drawing, if f(x) increases also f(x)+2 increases, whereas if f(x) increases, then g(x)=-0.5*f(x) decreases

29. Michele_Laino

oops..from my* last drawing...

30. anonymous

okay hahah! I see

31. Michele_Laino

I'm very sorry, it is 23:21 from me (Italy time zone) and I have to go to sleep

32. anonymous

Aww :( OK! I'll see if I can find someone else. Byeee<3

33. anonymous

Thanks so much!!!!

34. Michele_Laino

bye :) :)

35. Michele_Laino

thanks! :) :)

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