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anonymous

  • one year ago

Please help! The graph below shows a company's profit f(x), in dollars, depending on the price of notebooks x, in dollars, being sold by the company: Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? Part B: At one time the profit of the company was at least $220, what domain could possibly produce this profit? Part C: What is an approximate average rate of change of the graph from x = 2 to x = 4, and what does this rate represent?

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @Thesn1 can you please help I tried googling it and I cant find it

  3. anonymous
    • one year ago
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    @jim_thompson5910 hey can you help?

  4. jim_thompson5910
    • one year ago
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    how far did you get with this? did you get started at all?

  5. anonymous
    • one year ago
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    you want solution of all this or just the last question ??

  6. anonymous
    • one year ago
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    @jim_thompson5910 no I didn't start im confused with this topic

  7. jim_thompson5910
    • one year ago
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    what does x represent (this is given at the top) ?

  8. anonymous
    • one year ago
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    x is price of notebooks

  9. jim_thompson5910
    • one year ago
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    how about f(x) ?

  10. anonymous
    • one year ago
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    company's profit

  11. jim_thompson5910
    • one year ago
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    correct

  12. jim_thompson5910
    • one year ago
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    the x-intercepts are when f(x) = 0 so what does f(x) = 0 mean?

  13. anonymous
    • one year ago
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    that the company started at $0?

  14. jim_thompson5910
    • one year ago
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    not really "started" but just whenever the profit is $0 since f(x) = profit

  15. anonymous
    • one year ago
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    oh ok. so for part a the x intercepts are 0 and 4 right?

  16. jim_thompson5910
    • one year ago
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    correct, so what does that mean?

  17. anonymous
    • one year ago
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    ummmmmm. idk?

  18. jim_thompson5910
    • one year ago
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    when x = 0, the value of f(x) = 0 so when the price is $0, the profit is $0, agreed?

  19. anonymous
    • one year ago
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    ya agree. so What do the x-intercepts and maximum value of the graph represent?

  20. jim_thompson5910
    • one year ago
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    what does the x intercept of 4 represent?

  21. anonymous
    • one year ago
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    the profit is $4?

  22. jim_thompson5910
    • one year ago
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    not quite

  23. anonymous
    • one year ago
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    then idk. im not good at quadratics

  24. jim_thompson5910
    • one year ago
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    when the price is $4, the profit is $0

  25. anonymous
    • one year ago
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    oh ok. so the x-intercepts are 0 and 4, and maximum value of the graph represent what?

  26. jim_thompson5910
    • one year ago
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    when they say "max value" they mean the max value of f(x) how big can f(x) get?

  27. anonymous
    • one year ago
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    300.

  28. jim_thompson5910
    • one year ago
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    yep so that is the max profit because again, f(x) is the profit

  29. jim_thompson5910
    • one year ago
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    what value of x corresponds to the max profit?

  30. anonymous
    • one year ago
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    ok and 2.

  31. jim_thompson5910
    • one year ago
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    yep so when x = 2, f(x) = 300 therefore, when the price is $2, the max profit is $300. This is where the company wants to aim

  32. anonymous
    • one year ago
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    ok that makes more sense. ok and then for part a still What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?

  33. jim_thompson5910
    • one year ago
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    the function is increasing if you are going uphill as you go from left to right decreasing is the opposite way (downhill) as you go from left to right

  34. jim_thompson5910
    • one year ago
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    |dw:1433120212372:dw|

  35. jim_thompson5910
    • one year ago
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    |dw:1433120219258:dw|

  36. jim_thompson5910
    • one year ago
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    |dw:1433120232720:dw|

  37. anonymous
    • one year ago
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    ok so what would I put for part a answer?

  38. jim_thompson5910
    • one year ago
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    for the increasing/decreasing part, they just want the intervals along the x axis

  39. jim_thompson5910
    • one year ago
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    for example (this is not the answer, just an example) say we had this scale |dw:1433120434137:dw| the increasing interval would be from x = 0 to x = 10 you can write that as 0 < x < 10 or in interval notation as (0,10) the decreasing interval would be from x = 10 to x = 20 you can write that as 10 < x < 20 or in interval notation as (10,20)

  40. anonymous
    • one year ago
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    i don't get it. @jim_thompson5910

  41. jim_thompson5910
    • one year ago
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    where are you stuck at

  42. anonymous
    • one year ago
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    i just don't understand what you just said for the intervals.

  43. jim_thompson5910
    • one year ago
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    do you see how on my example graph, the curve goes uphill as you go from left to right until you hit x = 10?

  44. anonymous
    • one year ago
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    ya

  45. jim_thompson5910
    • one year ago
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    so that's how I got the interval from 0 to 10 0 < x < 10 basically when x is between 0 and 10, the graph is going uphill...ie increasing

  46. anonymous
    • one year ago
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    oh ok so for my graph, it would be 0<x<300 right?

  47. anonymous
    • one year ago
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    for increasing. and then i don't know about decreasing

  48. jim_thompson5910
    • one year ago
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    actually 0 < x < 2 look along the x axis (not y)

  49. anonymous
    • one year ago
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    ohhhhhh. so what would the decreasing be?

  50. jim_thompson5910
    • one year ago
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    give it a shot

  51. jim_thompson5910
    • one year ago
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    hopefully you see how I'm getting 0 < x < 2 ?

  52. anonymous
    • one year ago
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    2<x<50?

  53. jim_thompson5910
    • one year ago
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    that's a possibility, but to be really practical, the company only cares about when the profit is 0 or positive (ideally when it's positive) so it would be from x = 2 to x = 4. Anything beyond x = 4 is territory the company doesn't want to go into so that's why it's practical to say 2 < x < 4 is the interval in which the function is decreasing. In a practical context anyway

  54. jim_thompson5910
    • one year ago
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    notice how with the increasing part, I ignored everything to the left of x = 0

  55. anonymous
    • one year ago
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    ya. ok so i just have to look at the x axis right? when i do this

  56. jim_thompson5910
    • one year ago
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    yeah whenever looking at intervals of decreasing or increasing

  57. anonymous
    • one year ago
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    ok got it! thanks i do flvs and its hard to do algebra online. anyways, to answer the whole part of part a, how would i put it as

  58. jim_thompson5910
    • one year ago
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    Simply state in your own words the things we went over the roots, the max, the increasing/decreasing intervals

  59. anonymous
    • one year ago
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    but itt also says what does it represent and idk what to put for that

  60. anonymous
    • one year ago
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    Part B: At one time the profit of the company was at least $220, what domain could possibly produce this profit? @jim_thompson5910

  61. anonymous
    • one year ago
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    @jim_thompson5910 can you help me with part b and c!!??

  62. jim_thompson5910
    • one year ago
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    draw a horizontal line through y = 220 where does this horizontal line cross the parabola? at what two points?

  63. anonymous
    • one year ago
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    how do i do that?

  64. jim_thompson5910
    • one year ago
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  65. anonymous
    • one year ago
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    ok so (1,220) and (3,220)

  66. jim_thompson5910
    • one year ago
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    yes

  67. jim_thompson5910
    • one year ago
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    so the profit is at least $220 when x is between 1 and 3 (inclusive) \[\Large 1 \le x \le 3\]

  68. jim_thompson5910
    • one year ago
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    if the company wants a profit of $220 or greater, then it needs to have the price between $1 and $3

  69. anonymous
    • one year ago
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    ok so that would be my answer?

  70. jim_thompson5910
    • one year ago
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    yeah the domain is another way of asking for an interval

  71. jim_thompson5910
    • one year ago
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    do you see how to do part C?

  72. anonymous
    • one year ago
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    um no i need help with this sorry

  73. jim_thompson5910
    • one year ago
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    what are the two points on the parabola when x = 2 and x = 4?

  74. anonymous
    • one year ago
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    x= 2 is 300? and x=4 0?

  75. jim_thompson5910
    • one year ago
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    yep so we have the two points (2,300) and (4,0)

  76. jim_thompson5910
    • one year ago
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    what is the slope of the line through those two points?

  77. anonymous
    • one year ago
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    would it be a decreasing line

  78. jim_thompson5910
    • one year ago
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    yes the slope is some negative number

  79. anonymous
    • one year ago
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    ok so what would my answer be, A negative line that goes through 2,300 and 4,0

  80. jim_thompson5910
    • one year ago
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    use the slope formula \[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

  81. jim_thompson5910
    • one year ago
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    what slope do you get?

  82. anonymous
    • one year ago
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    um one second let me solve it

  83. anonymous
    • one year ago
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    -150

  84. jim_thompson5910
    • one year ago
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    correct

  85. jim_thompson5910
    • one year ago
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    so the average rate of change from x = 2 to x = 4 is -150 what does this mean? it means that the profit decreased by an average of $150 per increase of the price by $1 (ie each time the price went up $1, the profit dropped by $150)

  86. anonymous
    • one year ago
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    ok so -150 is the approximate average rate of change. and this rate represents what? so i put that down?

  87. jim_thompson5910
    • one year ago
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    yeah in your own words of course

  88. anonymous
    • one year ago
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    ya ik that. thanks so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  89. jim_thompson5910
    • one year ago
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    you're welcome

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