## anonymous one year ago x g(x) −2 2 −1 −3 0 2 1 17 Which of the following is a true statement for this function? The function is increasing from x = −2 to x = −1. The function is increasing from x = 0 to x = 1. The function is decreasing from x = −1 to x = 0. The function is decreasing from x = 0 to x = 1.

1. anonymous

I think its A

2. anonymous

@LynFran

3. anonymous

@Luigi0210

4. anonymous

it's the second one, because the output of 0=2 and the output of 1=17, so it is increasing from 0 to 1

5. anonymous

Okay, thanks!

6. anonymous

you're welcome :P

7. anonymous

Water coming out from a fountain is modeled by the function f(x) = −x2 + 6x + 6 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f(x) from x = 2 to x = 5 represent? The water travels an average distance of 4 feet from 2 seconds to 5 seconds. The water travels an average distance of 1 foot from 2 seconds to 5 seconds. The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds. The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds. @Nnesha

8. anonymous

make sure to medal XD

9. anonymous

I think the second one is D? I am just trying to check my answers ><

10. anonymous

If D was correct then it would make A true also... i'm pretty sure XD. From 2-5 seconds it would be a total of 4 seconds so if the water it traveling at 1 foot per second for 4 seconds, it would be a total of 4 feet.

11. anonymous

i think

12. Nnesha

average rate of change means slope the formula to find slope is $\huge\rm \frac{ y_2 -y_1 }{ x_2 -x_1 }$ given x=2 x=5 you have to find f(5) and f(2) so substitute x for 5 into f(x) function to find y

13. Nnesha

$\huge\rm f(x) = −x^2 + 6x + 6$ replace x with 5 and then with 2 solve let me know what you get

14. anonymous

f(x)=61 f(x)=22

15. Nnesha

nope try again

16. Nnesha

remember it's x^2 so it would be (2)^2

17. anonymous

So, would the number be negative? I confused now lol

18. Nnesha

show ur work how did you replaced x with 2 ?

19. anonymous

f(x)=-2^2 +6 x 2 + 6?

20. Nnesha

yes right

21. anonymous

So, then f(x)=-4+6 x 2 + 6?

22. anonymous

I see, they were supposed to remain negative

23. Nnesha

yes right! so final answer is what

24. anonymous

f(x)=-4 plus 12 plus 6 f(x)=8 plus 6 f(x)=14

25. Nnesha

yes right now replace x with 5

26. anonymous

f(x)=-25 plus 30 plus 6 f(x) = 5 plus 6 f(x)=11

27. Nnesha

yes right so order pairs are ( 2,14)(5,11) now plug them into the slope formula

28. anonymous

2^2-5^1 over 14^2 -11^1

29. Nnesha

ohh wait Y-2 means 2nd y not square

30. Nnesha

$\huge\rm (x_1 ,y_1) (1st ~x , 1st ~y)$

31. anonymous

wait what

32. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @gigirained 2^2-5^1 over 14^2 -11^1 $$\color{blue}{\text{End of Quote}}$$ it's not 14^2

33. Nnesha

|dw:1441384007239:dw|

34. Nnesha

$\huge\rm \frac{\color{reD}{ y_2} -y_1 }{ x_2 -x_1 }$ y_2 is just 11

35. anonymous

Ohh okay

36. Nnesha

so same with x_2 and x_1 substitute

37. anonymous

2-5 over 14 -11

38. anonymous

?

39. Nnesha

x should be at the denomiantor

40. Nnesha

denominator *

41. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @gigirained 2-5 over 14 -11 $$\color{blue}{\text{End of Quote}}$$ just flip it!

42. anonymous

Oh, alright, sorry i went to get water

43. Nnesha

lol

44. Nnesha

water is already in ur question lol solve that you will get the water

45. anonymous

haha, nice one

46. anonymous

so, i subtract and then divide or?

47. Nnesha

yes subtract then divide PEMDAS rules!

48. anonymous

so then, 14-11=3 and 2-5=-3 3/-3=-1?

49. Nnesha

yes right that's average rate it's negative so water would decrease or increase ?

50. anonymous

decrease

51. Nnesha

yes right !

52. Nnesha

falls down ugh samething

53. anonymous

lol yea

54. Nnesha

alright good to go! good luck!

55. anonymous

Thank you!

56. Nnesha

np!