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anonymous

  • one year ago

describe how to graph a piecewise-defined function.

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  1. anonymous
    • one year ago
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    @campbell_st

  2. e.mccormick
    • one year ago
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    Well.... do you know how to graph a function?

  3. anonymous
    • one year ago
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    explain using graphs and words

  4. e.mccormick
    • one year ago
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    Well, if you know how to do a graph, a piecewise one is just graphing the pieces.

  5. anonymous
    • one year ago
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    no i don't

  6. anonymous
    • one year ago
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    i am a beginner

  7. e.mccormick
    • one year ago
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    Hmmm... well, do yo know how say \(x^2\) is a parabola on a graph?

  8. anonymous
    • one year ago
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    |dw:1440462346722:dw|

  9. campbell_st
    • one year ago
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    well a parking station is an example of a piece wise graph or the cost of posting items there are limits for different conditions... e.g Parking fees free 0 < time <= 1 hour $1 1 < time < = 2 hours $3 2 < time <- 4 hours $10 time > 4 hours |dw:1440462065082:dw|

  10. anonymous
    • one year ago
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    ok

  11. anonymous
    • one year ago
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    that is understandable

  12. e.mccormick
    • one year ago
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    Sortof... And how y=x is just a line at a 45 degree angle that passes through 0. A piecewise is defined by some rules, so if I say: \(x^2 \text{ for } x \le 0\) \(x \text{ for } x > 0\) Then it is just both the parabola and the line and where they meet: |dw:1440462351205:dw|

  13. campbell_st
    • one year ago
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    so in extending this idea you can have |dw:1440462312993:dw|

  14. e.mccormick
    • one year ago
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    Here is better view of my graph: https://www.desmos.com/calculator/qduk9fxrbk

  15. anonymous
    • one year ago
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    thanks

  16. e.mccormick
    • one year ago
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    x^3! That is way up there. LOL.... but as campbell_st is pointing out, it also means they do not need to touch. https://www.desmos.com/calculator/6hl6ntxydl That is a graph of his last one.

  17. anonymous
    • one year ago
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    ohh

  18. e.mccormick
    • one year ago
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    If you look at that graph, you will see the x^3 part does not start until y=64! So between y= a little less than 16 to y=63.999999999999 etc. there is just no y values at all.

  19. anonymous
    • one year ago
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    @e.mccormick

  20. anonymous
    • one year ago
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    |dw:1440463601392:dw|

  21. anonymous
    • one year ago
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    so are those related to the car parking example

  22. anonymous
    • one year ago
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    @Nnesha

  23. anonymous
    • one year ago
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    are those related to the car parking example

  24. anonymous
    • one year ago
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    |dw:1440463703158:dw|

  25. anonymous
    • one year ago
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    @e.mccormick

  26. e.mccormick
    • one year ago
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    No, he did a different example to show some options. That is why I did the graph of that one on desmos as the last graph I did.

  27. anonymous
    • one year ago
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    what are the intervals of the park station example

  28. anonymous
    • one year ago
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    @e.mccormick

  29. anonymous
    • one year ago
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    |dw:1440464506395:dw|

  30. anonymous
    • one year ago
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    what are the intervals of the graph

  31. e.mccormick
    • one year ago
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    That part: Parking fees free 0 < time <= 1 hour $1 1 < time < = 2 hours $3 2 < time <- 4 hours $10 time > 4 hours

  32. anonymous
    • one year ago
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    yes

  33. e.mccormick
    • one year ago
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    I am saying that those are the intervals he graphed.

  34. anonymous
    • one year ago
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    ok

  35. anonymous
    • one year ago
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    |dw:1440465233293:dw| what is that arrow?

  36. anonymous
    • one year ago
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    what is that arrow

  37. anonymous
    • one year ago
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    @e.mccormick

  38. e.mccormick
    • one year ago
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    It keeps going.

  39. anonymous
    • one year ago
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    |dw:1440465386630:dw|

  40. anonymous
    • one year ago
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    i want the intervals to be written like that

  41. e.mccormick
    • one year ago
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    $10 time > 4 hours The > means, "From this point and one second more on to it stays there forever, it is $10." So on the graph you use an arrow.

  42. e.mccormick
    • one year ago
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    that is the other one I graphed.

  43. anonymous
    • one year ago
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    how do we identify the intervals

  44. anonymous
    • one year ago
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    what is the domain for the example

  45. anonymous
    • one year ago
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    |dw:1440465552670:dw|

  46. anonymous
    • one year ago
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    what is the domain?

  47. anonymous
    • one year ago
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    domain and range?

  48. e.mccormick
    • one year ago
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    The domain is the valid set of input variables. So, what is the minimum ammount of time you can park a car?

  49. anonymous
    • one year ago
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    1 hr

  50. anonymous
    • one year ago
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    yup it is 1hr

  51. anonymous
    • one year ago
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    for 1 hr it is free

  52. e.mccormick
    • one year ago
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    Nope. It has 0 there... so if a person pulls in, urns arounf, and leaves they have parked for 0 time.

  53. anonymous
    • one year ago
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    so the domain is x=0

  54. e.mccormick
    • one year ago
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    Starts at 0. It ends at the maximum time you can park.

  55. anonymous
    • one year ago
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    x=infinite

  56. e.mccormick
    • one year ago
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    fyi: It is normally done with a brace: \(f(x)\begin{cases} 2x+3 & \text{, } x<0 \\ x^2 & \text{, } x\le x < 4 \\ x^3 & \text{, } x\ge 4 \end{cases} \)

  57. anonymous
    • one year ago
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    can you write the steps of graphing the piece wise function?

  58. e.mccormick
    • one year ago
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    So the domain is from 0 to infinity.

  59. anonymous
    • one year ago
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    so the domain is the braces one?

  60. e.mccormick
    • one year ago
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    The steps are the same as any graph, but there are restrictions on how long you need to draw each part. The domain can be written several ways. You might use the union/intersection signs (cup and cap), or you might use interval notation or you might write it out long hand... depends on what the instructor wants.

  61. anonymous
    • one year ago
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    the question is "In your own words, describe how to graph a piecewise-defined function."

  62. anonymous
    • one year ago
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    so plzz help

  63. e.mccormick
    • one year ago
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    Like I said, you graph each part, but you need to keep track of where you start and stop.

  64. e.mccormick
    • one year ago
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    http://www.coolmath.com/algebra/21-advanced-graphing/03-piecewise-functions-01

  65. anonymous
    • one year ago
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    but, the braces one is the domain right?

  66. e.mccormick
    • one year ago
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    Yes. So \([0, \infty)\) for domain. The range would be set in that example. There are only 4 y values.

  67. anonymous
    • one year ago
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    ok

  68. anonymous
    • one year ago
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    (0,1,3,10)

  69. anonymous
    • one year ago
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    that is the range right?

  70. anonymous
    • one year ago
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    set of y values

  71. anonymous
    • one year ago
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    can you do the other problem for me?

  72. anonymous
    • one year ago
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    I tagged you

  73. e.mccormick
    • one year ago
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    That is the correct range.

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