1. Xaze

Compare the functions shown below:

2. Xaze

3. Xaze

What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = -1 to x = 3?

4. anonymous

the rate of change of that line is a constant it is the slope do you know it?

5. Xaze

@satellite73 Would 0.5/3 be the slope? I'm pretty bad at this, haha

6. Xaze

Sorry, 1.5*/3

7. Astrophysics

You have to find the slope of each function f(x), g(x), and h(x) $A(x)= \frac{ f(b)-f(a) }{ b-a }$ this is the average rate of change |dw:1440377631421:dw|

8. Astrophysics

So what is f(3) for f(x)?

9. Xaze

f(3)=((3)+3)^2-2, am I doing okay, so far?

10. Astrophysics

Yup, exactly!

11. Xaze

f(3)=(9)^2-2 - > f(3)=81-2 -> 79?

12. Astrophysics

Not quite, 3+3 = 6 :P

13. Xaze

Oh whoops... I was thinking of multiplication, for some reason.. f(3)=(6)^2-2 -> f(3)=36-2 - > f(3)=34?

14. Astrophysics

Yup that's good!

15. Astrophysics

now find f(-1)

16. Xaze

Yay! ^^

17. Astrophysics

@satellite73 hey if you want to take an image and upload it on draw which is very useful check out this guide on how to do it http://openstudy.com/users/astrophysics#/updates/55921cb5e4b0c2028eab5952 it's really quick to get it and helpful :P

18. Xaze

|dw:1440381614071:dw|

19. Astrophysics

perfect now we have $f(x) = \frac{ 34-2 }{ 3-(-1) }$

20. Xaze

$f(x)=32/4?$

21. Astrophysics

Yes simplify it

22. Astrophysics

I should say m = that not f(x) xD but same thing

23. Xaze

16/2

24. Astrophysics

m = 34/4 = 16/2 keep going

25. Xaze

8/1

26. Astrophysics

Yup m = 8 for f(x)

27. Astrophysics

|dw:1440378413551:dw| what are these two points?

28. Astrophysics

We're doing g(x) now

29. Xaze

Computer is slowing down - sorry, sorry x-x The two points are (-1,-2) and (3,0)

30. Astrophysics

Yup perfect, so use $m = \frac{ y_2-y_1 }{ x_2-x_1 }$ to find the slope |dw:1440378607899:dw| this is what it means visually

31. Xaze

All right... |dw:1440382384897:dw|

32. Astrophysics

Yes! 1/2 is good

33. Astrophysics

So we have slope for f(x) = 8, g(x) = 1/2, now lets find the slope for h(x)

34. Xaze

Not sure how to find the slope for that one... doesn't seem to be in my notes

35. Astrophysics

Just read the table and apply the formula

36. Astrophysics

|dw:1440379170633:dw|

37. Xaze

The formula $m=y2-y1/x2-x1$? Just making sure

38. Astrophysics

yup

39. Xaze

Okay, before I solve, how did you know to get (-1,14) and (3,62) from the chart? Or did you pick them randomly... and any pair you choose would give the same slope?

40. Astrophysics

No, because your question is asking for the average rate of change from x = -1 to x = 3, but it doesn't really matter, you'll get the same slope for any two points

41. Xaze

|dw:1440383049367:dw|

42. Astrophysics

Yes! Now we have the slopes f(x) = 8, g(x) = 1/2 and h(x) = 12 now put it least to greatest and we're done

43. Xaze

g(x),f(x), h(x)!

44. Astrophysics

Looks good :)

45. Xaze

Thanks so much, you're really a life-saver!

46. Astrophysics

Yw :)

47. Xaze

@Astrophysics, Do you think you can help with a few more? I'm almost finished with this test and I've got to get it submitted before midnight...

48. Astrophysics

Oh this was a test...we can't help on tests sorry.