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anonymous

  • one year ago

@jim_thompson5910

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  1. anonymous
    • one year ago
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    DESCRIBE EACH FUNCTION AS ONE OR MORE TRANSFORMATIONS OF IT'S PARENT FUNCTION 1. g(x) = log (x + 4) 2. g(x) = -x^2 - 3 3. g(x) = (2 / x +5) 4. g(x) = e ^(-4x)

  2. jim_thompson5910
    • one year ago
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    what's the parent function of g(x) = log (x + 4)

  3. anonymous
    • one year ago
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    let me graph it on my calc

  4. anonymous
    • one year ago
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    (0, 0.60)

  5. jim_thompson5910
    • one year ago
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    when I say "parent" function, I'm talking about the most basic form of it before you do any transformations

  6. jim_thompson5910
    • one year ago
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    example: x^2 is a parent function (x+2)^2 + 7 is a transformed version of the x^2 parent function

  7. anonymous
    • one year ago
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    idk

  8. jim_thompson5910
    • one year ago
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    here's a list of parent functions commonly used http://www.toomey.org/tutor/harolds_cheat_sheets/Harolds_Parent_Functions_Cheat_Sheet_2014.pdf

  9. jim_thompson5910
    • one year ago
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    they consist of the basic shapes you'll see in graphs example: x^2 has a bowl shape. Any other bowl shape graph is most likely based off the parent function of x^2

  10. anonymous
    • one year ago
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    oh okay so it would be a natural log

  11. jim_thompson5910
    • one year ago
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    or just log

  12. anonymous
    • one year ago
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    k

  13. jim_thompson5910
    • one year ago
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    I would say that log(x) is the parent of log (x + 4)

  14. anonymous
    • one year ago
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    that would be the answer for 1?

  15. jim_thompson5910
    • one year ago
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    how would you describe the transformation?

  16. anonymous
    • one year ago
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    like how it would look on a graph?

  17. jim_thompson5910
    • one year ago
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    yeah if you want, you can compare the parent function y = log(x) to y = log(x+4)

  18. jim_thompson5910
    • one year ago
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    how are those two different? how are they similar?

  19. anonymous
    • one year ago
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    they both start from a negative y and go up to a positive y moving to a greater number of x value?

  20. anonymous
    • one year ago
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    |dw:1443229687081:dw|

  21. anonymous
    • one year ago
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    |dw:1443229706167:dw|

  22. jim_thompson5910
    • one year ago
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    they have the same basic curve shape, yes

  23. anonymous
    • one year ago
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    like that

  24. jim_thompson5910
    • one year ago
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    the only difference is that log(x+4) is shifted 4 units to the left. You have the correct graphs

  25. jim_thompson5910
    • one year ago
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    you'll follow these same steps for 2 through 4

  26. anonymous
    • one year ago
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    oay cool i thin i got it can i try doing number 2 by my self

  27. jim_thompson5910
    • one year ago
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    go for it

  28. anonymous
    • one year ago
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    so number 2 in would be shifter 3 units down and fliped upside down

  29. jim_thompson5910
    • one year ago
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    you actually flip first, then shift 3 units down

  30. jim_thompson5910
    • one year ago
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    the order matters (if you want, cut out a parabolic shape on paper, and play around with the 2 orders)

  31. jim_thompson5910
    • one year ago
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    parent: x^2 flip over x axis: x^2 -----> -x^2 shift down 3 units: -x^2 -----> -x^2 - 3

  32. anonymous
    • one year ago
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    oh ok

  33. anonymous
    • one year ago
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    3 would go from this |dw:1443230322910:dw| to this

  34. anonymous
    • one year ago
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    |dw:1443230407412:dw|

  35. jim_thompson5910
    • one year ago
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    3 is this right? \[\Large \frac{2}{x+5}\]

  36. anonymous
    • one year ago
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    yup

  37. anonymous
    • one year ago
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    would it be the one of the negative x values shifted 5 units up and the one in the positive value shifted 5 units down

  38. jim_thompson5910
    • one year ago
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    what is the parent function here

  39. anonymous
    • one year ago
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    1/x

  40. jim_thompson5910
    • one year ago
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    when we go to 2/x, what happens to the graph?

  41. anonymous
    • one year ago
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    the ones in the negative x valuves move 2 unites to the left and vice versa

  42. jim_thompson5910
    • one year ago
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    how are you graphing these functions? on paper? or with a graphing calculator?

  43. anonymous
    • one year ago
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    calc

  44. anonymous
    • one year ago
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    oh and it will also move down

  45. jim_thompson5910
    • one year ago
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    I'm using desmos if you want to use that here's the link https://www.desmos.com/calculator

  46. jim_thompson5910
    • one year ago
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    here are 1/x and 2/x plotted together https://www.desmos.com/calculator/mgo61oouia

  47. jim_thompson5910
    • one year ago
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    what differences do you see?

  48. anonymous
    • one year ago
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    it moves half a unit

  49. jim_thompson5910
    • one year ago
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    well stretching is being done here. Vertical stretching by a factor of 2

  50. jim_thompson5910
    • one year ago
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    eg: (1,1) on 1/x turns into (1,2) on 2/x

  51. jim_thompson5910
    • one year ago
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    then notice how the green graph is shifted 5 units to the left to get 2/(x+5) https://www.desmos.com/calculator/ul6qdzno6d

  52. anonymous
    • one year ago
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    oh okay i see

  53. anonymous
    • one year ago
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    for the last one would it ve a vertical flip and shifts 4 units to he right

  54. jim_thompson5910
    • one year ago
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    no, that would be true if it were e^(x-4)

  55. jim_thompson5910
    • one year ago
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    we start with e^x which is the parent function replace the x with -4x. That will do 2 things a) the negative flips the graph over the y axis b) the 4 horizontally compresses the graph by a factor of 4 https://www.desmos.com/calculator/5tkhkrwm5e

  56. jim_thompson5910
    • one year ago
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    if in doubt, graph to check

  57. anonymous
    • one year ago
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    oh ookkk

  58. anonymous
    • one year ago
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    than you so much

  59. jim_thompson5910
    • one year ago
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    np

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