## mathmath333 one year ago Identifying Graphical function

1. mathmath333

|dw:1435071288021:dw|

2. mathmath333

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

$$a$$ is wrong because the graph is not symmetric about origin $$b$$ is wrong because the graph is not symmetric about $$y$$ axis

4. ganeshie8

i go wid $$c$$

5. mathmath333

but how did u concluded that

6. ganeshie8

the graph passes vertical line test, so it is actually a function. so $$d$$ is also wrong.

7. ganeshie8

or are you asking how to conclude it is not symmetric about origin ?

8. mathmath333

i mean how u judged that the function exists at all points ?

9. mathmath333

and also what is vertical line test

10. ganeshie8

lets rephrase that question : how do you know that the graph is a function ?

11. ganeshie8

it is essential to know the difference between a "relation" and a "function"

12. mathmath333

ok

13. ganeshie8

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

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

ok i get that relation can have multiple x values for y , but a function cannot

16. ganeshie8

yes is below graph a function or just a relation |dw:1435073159068:dw|

17. ganeshie8

how do you know it

18. mathmath333

rellation but not function

19. mathmath333

cuz we have 2 different y values for same x value

20. ganeshie8

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

|dw:1435073363932:dw|

22. mathmath333

ok i get that VLT

23. ganeshie8

lets get back to the actual graph, is it passing vertical line test ?

24. ganeshie8

|dw:1435073452344:dw|

25. mathmath333

yes it passes VLT but for negative values of x there is not y values such as this line

26. mathmath333

|dw:1435073568393:dw|

27. ganeshie8

that means the function is defined only for x > 0

28. mathmath333

so it is undefined for x<0 ?

29. mathmath333

then it should be option d.)

30. ganeshie8

x<0 is not part of the domain, so d is wrong.

31. mathmath333

ok i get that thanks

32. mathmath333

33. mathmath333

is it also option C.)

34. ganeshie8

Yes

35. mathmath333

36. mathmath333

is is even

37. ganeshie8

Yes notice that it is symmetric about $$y$$ axis |dw:1435074436000:dw|

38. ganeshie8

$\large f(x) = f(-x)$

39. mathmath333

|dw:1435074719834:dw|

40. mathmath333

is it option d.)

41. ganeshie8

nope, it is a function check whether it is odd/even

42. mathmath333

but it fails vertical line test at $$x=0$$ ?

43. ganeshie8

why ? it is well defined at x = 0 f(0) = 0 right ?

44. mathmath333

and what about the points |dw:1435075038716:dw|

45. ganeshie8

look at the graph like this : |dw:1435075017594:dw|

46. mathmath333

but that graph u draw looks different from the original one

47. ganeshie8

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

ok

49. mathmath333

so it is odd function

50. ganeshie8

Yes how did u figure out it is odd ?

51. mathmath333

because it is symmetrical with respect to origin

52. mathmath333

is the reason correct

53. ganeshie8

Yep! |dw:1435075546512:dw|

54. mathmath333

|dw:1435075812493:dw|

55. mathmath333

this is option C

56. ganeshie8

does it pass vertical line test ?

57. mathmath333

no it should be option d.

58. mathmath333

|dw:1435075996061:dw|

59. mathmath333

this is option c.)

60. ganeshie8

does it pass vertical line test ?

61. ganeshie8

|dw:1435076100827:dw|

62. mathmath333

lol no it doesnt pass

63. ganeshie8

so that graph does not represent a function

64. mathmath333

|dw:1435076275748:dw|

65. mathmath333

this is odd function ?

66. ganeshie8

Yes

67. mathmath333

do i need to check further if equation of the graph is given

68. dan815

id go with C too

69. dan815

the function can do anything beyond what u dont see so u cant say its undefined at some domain

70. dan815

|dw:1435076708335:dw|

71. dan815

what u do know is that its not mirrored across the y axis or x and y axis

72. dan815

|dw:1435076754260:dw|

73. mathmath333

but this works fine so far (looks odd function) https://www.desmos.com/calculator/zenrcqo1cg

74. ganeshie8

|dw:1435076810329:dw|

75. mathmath333

oh i see that is neat trick

76. mathmath333

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77. ganeshie8

lets change option d to a more meaningful one : d) not a function. only a relation.

78. mathmath333

|dw:1435077115505:dw|

79. ganeshie8

im not so comfortable with the phrase : "f(x) doesn't exist..."

80. mathmath333

|dw:1435077115505:dw|

81. ganeshie8

|dw:1435077393446:dw|

82. mathmath333

|dw:1435077588951:dw| ok this looks odd function

83. mathmath333

f(x)=f(-x)

84. mathmath333

|dw:1435077669264:dw| this too is odd function ?

85. ganeshie8

Yes

86. mathmath333

|dw:1435077791382:dw| this is which type of function

87. mathmath333

this looks odd for me

88. ganeshie8

sure ?

89. mathmath333

yes,why ?

90. ganeshie8

it is not an odd function $\large f(x) =\lfloor x\rfloor$

91. ganeshie8

Is below really true ?$\large \lfloor x\rfloor =-\lfloor -x\rfloor$ ?

92. mathmath333

this is greatest integer function ?

93. ganeshie8

looks like it

94. ganeshie8

|dw:1435078161945:dw|

95. mathmath333

$$\large{ \lfloor 2.5\rfloor=2\\ -\lfloor -2.5\rfloor=-\lfloor 2\rfloor}=-2$$ so this looks odd if it is GIF

96. mathmath333

|dw:1435078351737:dw|

97. ganeshie8

are you sure $$\large \lfloor -2.5\rfloor = -2$$ ?

98. mathmath333

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

$$\large \lfloor -2.5\rfloor = -3$$

100. ganeshie8

-3 is the smallest neighbor integer for -2.5

101. xapproachesinfinity

how do you plot floor and ceiling with goegebra or some other programs

102. xapproachesinfinity

i got it you just right floor :)

103. ganeshie8

yes f(x)=floor(x) works just fine :)

104. xapproachesinfinity

it does not let me do f(x)=floor(x)+x for example