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mathmath333

  • one year ago

Identifying Graphical function

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  1. mathmath333
    • one year ago
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    |dw:1435071288021:dw|

  2. mathmath333
    • one year ago
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    graph is \(\large \color{black}{\begin{align} &a.) \ f(x)=-f(x) \hspace{.33em}\\~\\ &b.) \ f(x)=f(-x) \hspace{.33em}\\~\\ &c.) \ \normalsize \text{neither even nor odd function} \hspace{.33em}\\~\\ &d.) \ f(x)\ \normalsize \text{doesn't exist at atleast one point of the domain.} \hspace{.33em}\\~\\ \end{align}}\)

  3. ganeshie8
    • one year ago
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    \(a\) is wrong because the graph is not symmetric about origin \(b\) is wrong because the graph is not symmetric about \(y\) axis

  4. ganeshie8
    • one year ago
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    i go wid \(c\)

  5. mathmath333
    • one year ago
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    but how did u concluded that

  6. ganeshie8
    • one year ago
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    the graph passes vertical line test, so it is actually a function. so \(d\) is also wrong.

  7. ganeshie8
    • one year ago
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    or are you asking how to conclude it is not symmetric about origin ?

  8. mathmath333
    • one year ago
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    i mean how u judged that the function exists at all points ?

  9. mathmath333
    • one year ago
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    and also what is vertical line test

  10. ganeshie8
    • one year ago
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    lets rephrase that question : how do you know that the graph is a function ?

  11. ganeshie8
    • one year ago
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    it is essential to know the difference between a "relation" and a "function"

  12. mathmath333
    • one year ago
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    ok

  13. ganeshie8
    • one year ago
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    relation is just about anything, for example : the relation showing friends of a student in your class is a relation \[\{\text{(suresh, krishna), (rajesh, mahes), (suresh, rama), }\cdots\}\]

  14. ganeshie8
    • one year ago
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    A function is also relation in which every input points to exactly one output. Above relation is NOT a function because \(\text{suresh}\) is pointing to two different students \(\text{krishna}\) and \(\text{rama}\)

  15. mathmath333
    • one year ago
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    ok i get that relation can have multiple x values for y , but a function cannot

  16. ganeshie8
    • one year ago
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    yes is below graph a function or just a relation |dw:1435073159068:dw|

  17. ganeshie8
    • one year ago
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    how do you know it

  18. mathmath333
    • one year ago
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    rellation but not function

  19. mathmath333
    • one year ago
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    cuz we have 2 different y values for same x value

  20. ganeshie8
    • one year ago
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    that is also called vertical line test, sweep a vertical line from left to right if the graph touches the vertical line at two different places, then the graph is not a function

  21. ganeshie8
    • one year ago
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    |dw:1435073363932:dw|

  22. mathmath333
    • one year ago
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    ok i get that VLT

  23. ganeshie8
    • one year ago
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    lets get back to the actual graph, is it passing vertical line test ?

  24. ganeshie8
    • one year ago
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    |dw:1435073452344:dw|

  25. mathmath333
    • one year ago
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    yes it passes VLT but for negative values of x there is not y values such as this line

  26. mathmath333
    • one year ago
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    |dw:1435073568393:dw|

  27. ganeshie8
    • one year ago
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    that means the function is defined only for x > 0

  28. mathmath333
    • one year ago
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    so it is undefined for x<0 ?

  29. mathmath333
    • one year ago
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    then it should be option d.)

  30. ganeshie8
    • one year ago
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    x<0 is not part of the domain, so d is wrong.

  31. mathmath333
    • one year ago
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    ok i get that thanks

  32. mathmath333
    • one year ago
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    what about this graph |dw:1435074083721:dw|

  33. mathmath333
    • one year ago
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    is it also option C.)

  34. ganeshie8
    • one year ago
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    Yes

  35. mathmath333
    • one year ago
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    |dw:1435074325926:dw| what about this graph

  36. mathmath333
    • one year ago
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    is is even

  37. ganeshie8
    • one year ago
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    Yes notice that it is symmetric about \(y\) axis |dw:1435074436000:dw|

  38. ganeshie8
    • one year ago
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    \[\large f(x) = f(-x)\]

  39. mathmath333
    • one year ago
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    |dw:1435074719834:dw|

  40. mathmath333
    • one year ago
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    is it option d.)

  41. ganeshie8
    • one year ago
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    nope, it is a function check whether it is odd/even

  42. mathmath333
    • one year ago
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    but it fails vertical line test at \(x=0\) ?

  43. ganeshie8
    • one year ago
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    why ? it is well defined at x = 0 f(0) = 0 right ?

  44. mathmath333
    • one year ago
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    and what about the points |dw:1435075038716:dw|

  45. ganeshie8
    • one year ago
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    look at the graph like this : |dw:1435075017594:dw|

  46. mathmath333
    • one year ago
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    but that graph u draw looks different from the original one

  47. ganeshie8
    • one year ago
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    f(0) = 0 all other points are not part of the graph because the question clearly says f(x) = 0 at x=0

  48. mathmath333
    • one year ago
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    ok

  49. mathmath333
    • one year ago
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    so it is odd function

  50. ganeshie8
    • one year ago
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    Yes how did u figure out it is odd ?

  51. mathmath333
    • one year ago
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    because it is symmetrical with respect to origin

  52. mathmath333
    • one year ago
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    is the reason correct

  53. ganeshie8
    • one year ago
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    Yep! |dw:1435075546512:dw|

  54. mathmath333
    • one year ago
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    |dw:1435075812493:dw|

  55. mathmath333
    • one year ago
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    this is option C

  56. ganeshie8
    • one year ago
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    does it pass vertical line test ?

  57. mathmath333
    • one year ago
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    no it should be option d.

  58. mathmath333
    • one year ago
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    |dw:1435075996061:dw|

  59. mathmath333
    • one year ago
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    this is option c.)

  60. ganeshie8
    • one year ago
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    does it pass vertical line test ?

  61. ganeshie8
    • one year ago
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    |dw:1435076100827:dw|

  62. mathmath333
    • one year ago
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    lol no it doesnt pass

  63. ganeshie8
    • one year ago
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    so that graph does not represent a function

  64. mathmath333
    • one year ago
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    |dw:1435076275748:dw|

  65. mathmath333
    • one year ago
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    this is odd function ?

  66. ganeshie8
    • one year ago
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    Yes

  67. mathmath333
    • one year ago
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    do i need to check further if equation of the graph is given

  68. dan815
    • one year ago
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    id go with C too

  69. dan815
    • one year ago
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    the function can do anything beyond what u dont see so u cant say its undefined at some domain

  70. dan815
    • one year ago
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    |dw:1435076708335:dw|

  71. dan815
    • one year ago
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    what u do know is that its not mirrored across the y axis or x and y axis

  72. dan815
    • one year ago
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    |dw:1435076754260:dw|

  73. mathmath333
    • one year ago
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    but this works fine so far (looks odd function) https://www.desmos.com/calculator/zenrcqo1cg

  74. ganeshie8
    • one year ago
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    |dw:1435076810329:dw|

  75. mathmath333
    • one year ago
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    oh i see that is neat trick

  76. mathmath333
    • one year ago
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    |dw:1435077093925:dw|

  77. ganeshie8
    • one year ago
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    lets change option d to a more meaningful one : d) not a function. only a relation.

  78. mathmath333
    • one year ago
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    |dw:1435077115505:dw|

  79. ganeshie8
    • one year ago
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    im not so comfortable with the phrase : "f(x) doesn't exist..."

  80. mathmath333
    • one year ago
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    |dw:1435077115505:dw|

  81. ganeshie8
    • one year ago
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    |dw:1435077393446:dw|

  82. mathmath333
    • one year ago
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    |dw:1435077588951:dw| ok this looks odd function

  83. mathmath333
    • one year ago
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    f(x)=f(-x)

  84. mathmath333
    • one year ago
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    |dw:1435077669264:dw| this too is odd function ?

  85. ganeshie8
    • one year ago
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    Yes

  86. mathmath333
    • one year ago
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    |dw:1435077791382:dw| this is which type of function

  87. mathmath333
    • one year ago
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    this looks odd for me

  88. ganeshie8
    • one year ago
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    sure ?

  89. mathmath333
    • one year ago
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    yes,why ?

  90. ganeshie8
    • one year ago
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    it is not an odd function \[\large f(x) =\lfloor x\rfloor\]

  91. ganeshie8
    • one year ago
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    Is below really true ?\[\large \lfloor x\rfloor =-\lfloor -x\rfloor \] ?

  92. mathmath333
    • one year ago
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    this is greatest integer function ?

  93. ganeshie8
    • one year ago
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    looks like it

  94. ganeshie8
    • one year ago
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    |dw:1435078161945:dw|

  95. mathmath333
    • one year ago
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    \(\large{ \lfloor 2.5\rfloor=2\\ -\lfloor -2.5\rfloor=-\lfloor 2\rfloor}=-2 \) so this looks odd if it is GIF

  96. mathmath333
    • one year ago
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    |dw:1435078351737:dw|

  97. ganeshie8
    • one year ago
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    are you sure \(\large \lfloor -2.5\rfloor = -2\) ?

  98. mathmath333
    • one year ago
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    yes the greatest integer function specifies that \(\lfloor x\rfloor\) will be equal to the smallest integer neighbouring to it.|dw:1435079336656:dw|

  99. ganeshie8
    • one year ago
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    \(\large \lfloor -2.5\rfloor = -3\)

  100. ganeshie8
    • one year ago
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    -3 is the smallest neighbor integer for -2.5

  101. xapproachesinfinity
    • one year ago
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    how do you plot floor and ceiling with goegebra or some other programs

  102. xapproachesinfinity
    • one year ago
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    i got it you just right floor :)

  103. ganeshie8
    • one year ago
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    yes `f(x)=floor(x)` works just fine :)

  104. xapproachesinfinity
    • one year ago
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    it does not let me do f(x)=floor(x)+x for example

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