## anonymous one year ago Solve the problem, If f(x)= x-3A/3x+5 and f(3)=6. what is the value of A?

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1. anonymous

@jim_thompson5910

2. jim_thompson5910

this is f(x), right? $\Large f(x) = \frac{x-3A}{3x+5}$

3. anonymous

Correct

4. jim_thompson5910

$\Large f(x) = \frac{x-3A}{3x+5}$ $\Large f(3) = \frac{3-3A}{3(3)+5}$ $\Large 6 = \frac{3-3A}{3(3)+5}$ $\Large 6 = \frac{3-3A}{14}$ $\Large 14*6 = 14*\frac{3-3A}{14}$ $\Large 84 = 3-3A$ $\Large A = ??$

5. jim_thompson5910

In step 2, I replaced every x with 3 In step 3, I replaced f(3) with 6 (since f(3) = 6)

6. anonymous

Okay so I got A= -27

7. anonymous

|dw:1433980377815:dw|

8. anonymous

Use the accompanying graph of y=f(x) to sketch the graph of the indicated equation. Graph one transformation in each coordinate system.

9. anonymous

@jim_thompson5910

10. jim_thompson5910

f(-x) means you reflect over the y axis 2*f(-x) means you scale vertically, or stretch vertically, by a factor of 2

11. anonymous

How would I show this on the coordinate plane?

12. jim_thompson5910

start by reflecting each point over the y axis

13. anonymous

so it would be (-2,-2) and then? what?

14. jim_thompson5910

do the same for the other points as well

15. jim_thompson5910

|dw:1433981229533:dw|

16. jim_thompson5910

|dw:1433981248199:dw|

17. jim_thompson5910

imagine this happens to all of the points

18. jim_thompson5910

you'd get something like this |dw:1433981278828:dw|

19. anonymous

Okay :)

20. anonymous

and then? how would I do the second part?

21. jim_thompson5910

the 2* out front means you double each y coordinate

22. jim_thompson5910

ex: (2,-2) ----> (2,-4)

23. jim_thompson5910

ex: (2,-2) ----> (2,-4) |dw:1433981434340:dw| imagine this happens to EVERY point

24. anonymous

so I would show this for each point!

25. jim_thompson5910

yes

26. jim_thompson5910

and the overall graph

27. anonymous

Alright awesome thank you!

28. anonymous

ONe quick question

29. anonymous

Before you leave! :)

30. anonymous

If they ask me for which of the following values of x does f(x)=-20 and the graph is showing :|dw:1433981600730:dw|

31. jim_thompson5910

draw a horizontal line through y = -20 |dw:1433981843252:dw|

32. jim_thompson5910

then determine where that horizontal line crosses the curve

33. anonymous

(-25,15), (-15,0), (0,-15) , (10,-20) , (15,-10), (20,10) and (25,0)

34. anonymous

those are the points they provide!

35. anonymous

I know that -20 and 10 both have f(x)=-20

36. jim_thompson5910

hint: y = f(x)

37. anonymous

How would I determine the answer?

38. anonymous

@jim_thompson5910

39. jim_thompson5910

another hint: each point is of the form (x,y)

40. anonymous

Would I say {-20,10}

41. anonymous

This is all I could think of!

42. jim_thompson5910

(-20,10) means x = -20

43. jim_thompson5910

but they say f(x) = -20

44. anonymous

OKAY,,,, maybe I put it wrong? (-20,-20) and (10,-20)

45. jim_thompson5910

just look through the points (-25,15), (-15,0), (0,-15) , (10,-20) , (15,-10), (20,10) and (25,0) where the y coord is -20

46. jim_thompson5910

y = f(x) f(x) = -20 y = -20

47. anonymous

Okay so all I would say is (10,-20) correct?

48. anonymous

@jim_thompson5910

49. jim_thompson5910

yes that is the only point that fits the description

50. anonymous

okay... and sorry one last thing I PROMISE!!!

51. anonymous

iF I HAVE THE SAME coordinate plane but with different points and it is 20 instead of 25 and they ask for what numbers x is f(x)<0?

52. anonymous

How would I write this?

53. anonymous

It starts with -12 I know this but would it be [-12,-1]

54. anonymous

@jim_thompson5910

55. jim_thompson5910

can you post a screenshot of the full problem?

56. anonymous

|dw:1433982828860:dw|

57. anonymous

The graph of a function f is given. Use the graph to answer the question. (-20,12) , (-12,0) , (0,-12) , (8,-16) , (12, -8), (16,8) and (20,0)

58. anonymous

For what numbers x is f(x)<0 ?

59. jim_thompson5910

look at the points where the y coord is negative

60. jim_thompson5910

|dw:1433983055819:dw|

61. anonymous

Okay and they cant be greater than 0 correct?

62. jim_thompson5910

yeah because you said f(x) < 0

63. anonymous

Right so how would I say this?

64. jim_thompson5910

they just want you to list points?

65. anonymous

OKay so in this case it would be (-12,0)

66. jim_thompson5910

if that's the case, then list any points with y coordinates less than 0

67. anonymous

It asks me For what numbers x is f(x)<0

68. jim_thompson5910

what are the x intercepts of that graph

69. anonymous

-20 , -16, -12, -8, -4,0 4, 8, 12, 16 and 20

70. jim_thompson5910

|dw:1433983321114:dw|

71. anonymous

on the far left its -12 and on the far right its probably 14 because its in between 12 and 16

72. jim_thompson5910

|dw:1433983408801:dw|

73. anonymous

yes

74. jim_thompson5910

|dw:1433983425459:dw|

75. jim_thompson5910

|dw:1433983449734:dw|

76. anonymous

ok

77. anonymous

@jim_thompson5910

78. anonymous

???

79. anonymous

@jim_thompson5910 how would I write this?

80. anonymous

@jim_thompson5910

81. jim_thompson5910

I think they just want the x values that correspond to when y is negative

82. anonymous

So would I write something like [-12, -1]

83. jim_thompson5910

where are you getting -1?

84. anonymous

idk? I am guessing that this is correct? but I have no clue

85. anonymous

[-12, 14]

86. jim_thompson5910

the x intercepts are -12 and 14 the interval (-12,14) represents the region when f(x) < 0

87. anonymous

OKay thank you! but wouldnt it have to be [ instead of ( ?

88. jim_thompson5910

() because you don't include the points on the x axis

89. jim_thompson5910

not [ ]

90. anonymous

OKay I got cha awesome thank you so so so much your amazing :D

91. jim_thompson5910

yw