## kohai one year ago @hwyl

1. kohai

Domain and range looking at graphs

2. hwyl

oh okay go on

3. kohai

There is nothing to go on v,v I don't know how to do it

4. kohai

Omg satellite don't make fun of me ;-;

5. hwyl

oh okay we have domain co-domain range do you know each of those?

6. kohai

I saw that >.<

7. anonymous

i wasn't

8. anonymous

i was laughing at @hwyl

9. kohai

I know that domain is the x-values and range is the y. I can do it based off of coordinates but I can't do it based off of graphs

10. hwyl

oh okay that's fine create a graph for me do not label

11. anonymous

|dw:1443148507651:dw|

12. kohai

It's mostly the unlabled infinity graphs I have issues with

13. hwyl

just when I said do not label -_-

14. hwyl

let us do an example based off your book

15. kohai

16. hwyl

okay

17. hwyl

we're going to use the most basic cube function $$f(x) = x^3$$

18. kohai

Sure

19. hwyl

so what is the domain of the function?

20. kohai

$(-\infty, \infty)$ ?

21. hwyl

this is when you try to think about the pretty set-builder notation or that

22. hwyl

can x be any number?

23. kohai

I think so yeah

24. hwyl

think hard, what condition that it won't work

25. kohai

I feel really stupid for not knowing =.=

26. hwyl

we have Real numbers etc etc

27. kohai

Imaginary numbers? So like i and stuff I guess

28. hwyl

aha! there you go

29. anonymous

|dw:1443149075246:dw|

30. kohai

Yeah, the solid lines like that I'm okay with. It's stuff that I don't see an end to like parabolas and cubic graphs etc

31. hwyl

so pretty much any real number is valid

32. anonymous

|dw:1443149216613:dw|

34. kohai

@satellite73 , R=all real numbers?

35. kohai

This is where I start getting lost haha

36. hwyl

|dw:1443149291544:dw|

37. hwyl

since you were talking about infinities, let us try something periodic with infinity

38. hwyl

just pardon my drawing

39. kohai

You're pardoned ;)

40. hwyl

it's basically a graph of $$tan(x)$$

41. hwyl

suppose the domain, co-domain and range

42. hwyl

oops yes that!

43. hwyl

went too happy with the vertical lines

44. hwyl

|dw:1443149631927:dw|

45. hwyl

|dw:1443149780293:dw|

46. kohai

Pretty drawings

47. hwyl

let us see what the domain, range and period

48. kohai

I don't need to know period or co-domain. It's alg2 level rn

49. hwyl

oh so what is the domain and range?

50. kohai

domain [-pi/2, pi/2] range (-inf, inf)

51. hwyl

okay now think carefully does the x really cross or touch +/- pi/2

52. kohai

No

53. hwyl

so you can't really say $$\pm\pi/2$$

54. hwyl

maybe we can suppose that it is $$x \neq \pm \pi/2$$

55. kohai

v,v I won't have super complex domains and ranges on this test though

56. hwyl

oh okay then let us make it easier how about sin x draw the graph and indicate the domain and range

57. kohai

|dw:1443150342371:dw|

58. hwyl

make it a little smaller

59. kohai

Please tell me thats a sin graph...

60. kohai

ur jelly of my drawing skills

61. kohai

|dw:1443150458901:dw|

62. hwyl

|dw:1443150441508:dw|

63. hwyl

|dw:1443150577160:dw|

64. hwyl

65. kohai

Domain [0, inf) Range [1, -1]

66. hwyl

|dw:1443150722246:dw|

67. kohai

Oh. (-inf, inf)

68. hwyl

yes, because there is no constraint in the value of x provided that we use Real number

69. hwyl

@iambatman we need to do polarization later

70. hwyl

always from left to right or least to most so negative to positive

71. kohai

Gotcha, okay

72. hwyl

you pretty much get it already

73. kohai

Yeah I guess so. I just have to think about them. I can do linear because I can physically see, stuff with infinity is a bit more abstract

74. hwyl

|dw:1443151574827:dw|

75. hwyl

76. kohai

For some reason this puzzles me ;-;

77. hwyl

78. kohai

That's the part that's confusing me....... this is stupid v,v lol

79. hwyl

|dw:1443151869375:dw|

80. hwyl

can my range go lower than a?

81. kohai

No

82. hwyl

83. kohai

Oh I guess that makes sense. I got the 1 but I wasn't sure about the second coordinate

84. hwyl

I mean range:[a, inf)

85. hwyl

pellet, I was going to ask you about the one with the detailed function

86. hwyl

instead of an actual number, I assigned a

87. kohai

Lol

88. hwyl

but they are the same |dw:1443152138070:dw||dw:1443152147095:dw|

89. hwyl

you said earlier that domain is x and range is y |dw:1443152218860:dw|

90. hwyl

these are specific domains x, which gives you a range |dw:1443152497889:dw|

91. kohai

Gotcha

92. hwyl

but see, no matter what values you have for x, your y can only go up from 1

93. kohai

Hey I appreciate you helping me :)

94. hwyl

that's why our range starts from 1 to infinity

95. hwyl

that is because how the function is set up, constrained by the constant k |dw:1443152666861:dw|

96. hwyl

do you want me to get a few sample problems from a book?

97. kohai

Nah, I think I've got it. And even if I get like the 2 problems with domain and range wrong I know the rest of the stuff lol. I think I'll be fine. Thank you for helping me :)

98. hwyl

okay that's from a graph, how about from a function or equation?

99. kohai

Those I can do fine

100. kohai

And I'm starting to not process stuff lol. I think I'm good for now

101. hwyl

$$\large f(x) = \frac{1}{x^2-4}$$

102. hwyl

can you write your domain in set-builder notation?

103. kohai

Mehhh lemme look at some examples and come back to this

104. hwyl

wowwwww lol alright, I need to grab something to eat

105. kohai

I can't remember how to do it lol

106. hwyl

oh, you just need to remember the definition of a function

107. kohai

The y-coordinates can be the same, there just can't be more than one x-coordinate

108. hwyl

so your domain basically anything that the denominator will not be zero

109. kohai

So it can't be 2 or -2

110. hwyl

$$x^2 + 4 = 0$$ solve for x

111. hwyl

correct, so all real except for those two

112. kohai

How do I do that with notation?

113. hwyl

try

114. kohai

(-inf, -2] u [-2, 2] u [2, inf)

115. hwyl

$$x|x~ \epsilon~ \mathbb{R}, x \neq \pm 2$$

116. kohai

I think my teacher wants me to use that stupid u thing

117. hwyl

it is time for you to master it

118. hwyl

between pre-cal and cal, there's usually a program that helps you hone skills on logic and these notations

119. hwyl

inquire about it in your math department it will help a lot

120. kohai

Will do

121. hwyl

okay let us attempt to drive this home