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theopenstudyowl

  • one year ago

Math graphing help. Medals.

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  1. theopenstudyowl
    • one year ago
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    ;

  2. theopenstudyowl
    • one year ago
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    Its #4 only

  3. theopenstudyowl
    • one year ago
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    Anything?

  4. jim_thompson5910
    • one year ago
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    For #4, draw a vertical line through -4 on the x axis where does this vertical line cross the red f(x) curve?

  5. theopenstudyowl
    • one year ago
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    @ (-2,1) and (2,2)

  6. theopenstudyowl
    • one year ago
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    oh wait, sorry those are the points of intersection of the two functions, one sec.

  7. theopenstudyowl
    • one year ago
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    at x=3

  8. jim_thompson5910
    • one year ago
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    see attached

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  9. theopenstudyowl
    • one year ago
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    does this have to do with the vertical line test?

  10. jim_thompson5910
    • one year ago
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    no, I'm simply asking for the value of f(-4)

  11. theopenstudyowl
    • one year ago
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    oh

  12. theopenstudyowl
    • one year ago
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    Ok, could you help me with the domain and range part of the problem please.?

  13. jim_thompson5910
    • one year ago
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    so you figured out that part already? the f(-4) part?

  14. theopenstudyowl
    • one year ago
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    that wasnt the part I needed help with.. just included it because the graph is required in order to understand the rest of the problem..

  15. jim_thompson5910
    • one year ago
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    I see

  16. jim_thompson5910
    • one year ago
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    the domain is the set of allowed inputs, in other words, the set of allowed x values

  17. theopenstudyowl
    • one year ago
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    ok...

  18. jim_thompson5910
    • one year ago
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    the red f(x) function stretches from x = -4 to x = 4 the function is not defined for other x values (like x = 10)

  19. jim_thompson5910
    • one year ago
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    so that's why the domain is \[\Large -4 \le x \le 4\] in interval notation, the domain is written as `[-4, 4]` Notice the use of square brackets to mean include the endpoints

  20. jim_thompson5910
    • one year ago
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    what would be the domain of g(x) ?

  21. theopenstudyowl
    • one year ago
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    ok, I'll solve that now, could you explain to me when I include brackets and parenthesis when writing these things..?

  22. theopenstudyowl
    • one year ago
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    The domain of g(x) is [-4,3]

  23. jim_thompson5910
    • one year ago
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    the parenthesis are used to exclude the endpoint that's when you come across an endpoint with an open circle like so |dw:1440727842554:dw|

  24. jim_thompson5910
    • one year ago
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    |dw:1440727856238:dw|

  25. jim_thompson5910
    • one year ago
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    think of it as like a road that isn't finished. There is a pot hole at the open circle. It is NOT included in part of the road because you can't drive on it

  26. theopenstudyowl
    • one year ago
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    So when there is a circle, I use brackets?

  27. theopenstudyowl
    • one year ago
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    oh wait parenthesis nvm

  28. jim_thompson5910
    • one year ago
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    |dw:1440728130377:dw|

  29. theopenstudyowl
    • one year ago
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    ok thanks, could you help me with the range too plz?

  30. jim_thompson5910
    • one year ago
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    the range is the set of possible outputs of a function put another way, the range is the set of possible y values that could come out

  31. jim_thompson5910
    • one year ago
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    look at the red curve f(x) the lowest it goes is to y = -2 the highest it goes is to y = 3 the range of f(x) is \[\Large -2 \le y \le 3\] in interval notation the range of f(x) is `[-2,3]` I'll let you do g(x)

  32. theopenstudyowl
    • one year ago
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    ok, is my domain for g(x) correct?

  33. jim_thompson5910
    • one year ago
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    what did you say for the domain of g(x)?

  34. jim_thompson5910
    • one year ago
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    oh nvm, you wrote `The domain of g(x) is [-4,3]`

  35. jim_thompson5910
    • one year ago
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    yeah that is correct

  36. theopenstudyowl
    • one year ago
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    yah!

  37. theopenstudyowl
    • one year ago
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    ok, give me a sec for the other one...

  38. theopenstudyowl
    • one year ago
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    1/2 is less than or equal to y is less than or equal to 4

  39. jim_thompson5910
    • one year ago
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    I don't agree with the 1/2 part

  40. jim_thompson5910
    • one year ago
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    oh wait, nvm

  41. jim_thompson5910
    • one year ago
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    each tick is 1

  42. theopenstudyowl
    • one year ago
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    its hard to tell

  43. jim_thompson5910
    • one year ago
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    1/2 is a good estimate

  44. jim_thompson5910
    • one year ago
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    what would the range be in interval notation?

  45. theopenstudyowl
    • one year ago
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    [1/2,4]

  46. theopenstudyowl
    • one year ago
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    ?

  47. jim_thompson5910
    • one year ago
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    correct

  48. theopenstudyowl
    • one year ago
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    ok, cool, Could you explain to me when I use less than and less than or equal to, is there a clear way of knowing?

  49. jim_thompson5910
    • one year ago
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    it depends on if you have open or closed circles |dw:1440728925694:dw|

  50. jim_thompson5910
    • one year ago
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    when you include a point, you say "or equal to" eg: \[\Large x \le 5\] we're including 5

  51. jim_thompson5910
    • one year ago
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    saying `x > 5` we mean everything larger than 5 and we exclude 5 from the set

  52. theopenstudyowl
    • one year ago
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    ok cool, thanks!

  53. jim_thompson5910
    • one year ago
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    sure thing

  54. theopenstudyowl
    • one year ago
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    a) f(-4)=-2, g(3)=4. b) The values of x where f(x)=g(x) are x=-2 and x=2. c) An estimation of the solution of the equation f(x)=-1, is x=3. d) The interval on what f is decreasing is [0,4]. e) The domain of f(x) is [-4,4], the range of f(x) is [-2,3]. f) The domain of g(x) is [-4,3], the range of g(x) is [1/2,4].

  55. theopenstudyowl
    • one year ago
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    @jim_thompson5910 does anything look incorrect?

  56. jim_thompson5910
    • one year ago
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    `c) An estimation of the solution of the equation f(x)=-1, is x=3.` there's one other solution

  57. theopenstudyowl
    • one year ago
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    ok

  58. jim_thompson5910
    • one year ago
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    `d) The interval on what f is decreasing is [0,4].` f is not decreasing when x = 0 or at the endpoint x = 4 so you'll need to exclude the endpoints and say \(\Large (0,4)\)

  59. theopenstudyowl
    • one year ago
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    ok cool, does everything else look ok?

  60. jim_thompson5910
    • one year ago
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    everything else is perfect

  61. theopenstudyowl
    • one year ago
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    ok, and for c, how would I find that other point?

  62. jim_thompson5910
    • one year ago
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    draw a horizontal line through y = -1 and see where it crosses the red f(x) function

  63. jim_thompson5910
    • one year ago
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    you already found (3,-1)

  64. jim_thompson5910
    • one year ago
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    actually I think you meant to say (-3,-1)

  65. jim_thompson5910
    • one year ago
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    if f(x) = -1, then x = -3 or x = ???

  66. theopenstudyowl
    • one year ago
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    one sec

  67. theopenstudyowl
    • one year ago
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    and 4?

  68. jim_thompson5910
    • one year ago
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    yep

  69. theopenstudyowl
    • one year ago
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    so its x=-3 and 4?

  70. jim_thompson5910
    • one year ago
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    yes if f(x) = -1, then x = -3 or x = 4

  71. theopenstudyowl
    • one year ago
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    ok great, well thanks again for your wonderful help. Saved me alot of time, hope you have an awesome rest of your day!

  72. jim_thompson5910
    • one year ago
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    glad to be of help

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