## anonymous one year ago @hwyl

1. anonymous

Domain and range looking at graphs

2. anonymous

oh okay go on

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

I saw that >.<

7. anonymous

i wasn't

8. anonymous

i was laughing at @hwyl

9. anonymous

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. anonymous

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

11. anonymous

|dw:1443148507651:dw|

12. anonymous

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

13. anonymous

just when I said do not label -_-

14. anonymous

let us do an example based off your book

15. anonymous

16. anonymous

okay

17. anonymous

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

18. anonymous

Sure

19. anonymous

so what is the domain of the function?

20. anonymous

$(-\infty, \infty)$ ?

21. anonymous

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

22. anonymous

can x be any number?

23. anonymous

I think so yeah

24. anonymous

think hard, what condition that it won't work

25. anonymous

I feel really stupid for not knowing =.=

26. anonymous

we have Real numbers etc etc

27. anonymous

Imaginary numbers? So like i and stuff I guess

28. anonymous

aha! there you go

29. anonymous

|dw:1443149075246:dw|

30. anonymous

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. anonymous

so pretty much any real number is valid

32. anonymous

|dw:1443149216613:dw|

34. anonymous

@satellite73 , R=all real numbers?

35. anonymous

This is where I start getting lost haha

36. anonymous

|dw:1443149291544:dw|

37. anonymous

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

38. anonymous

just pardon my drawing

39. anonymous

You're pardoned ;)

40. anonymous

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

41. anonymous

suppose the domain, co-domain and range

42. anonymous

oops yes that!

43. anonymous

went too happy with the vertical lines

44. anonymous

|dw:1443149631927:dw|

45. anonymous

|dw:1443149780293:dw|

46. anonymous

Pretty drawings

47. anonymous

let us see what the domain, range and period

48. anonymous

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

49. anonymous

oh so what is the domain and range?

50. anonymous

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

51. anonymous

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

52. anonymous

No

53. anonymous

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

54. anonymous

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

55. anonymous

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

56. anonymous

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

57. anonymous

|dw:1443150342371:dw|

58. anonymous

make it a little smaller

59. anonymous

Please tell me thats a sin graph...

60. anonymous

ur jelly of my drawing skills

61. anonymous

|dw:1443150458901:dw|

62. anonymous

|dw:1443150441508:dw|

63. anonymous

|dw:1443150577160:dw|

64. anonymous

65. anonymous

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

66. anonymous

|dw:1443150722246:dw|

67. anonymous

Oh. (-inf, inf)

68. anonymous

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

69. anonymous

@iambatman we need to do polarization later

70. anonymous

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

71. anonymous

Gotcha, okay

72. anonymous

you pretty much get it already

73. anonymous

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. anonymous

|dw:1443151574827:dw|

75. anonymous

76. anonymous

For some reason this puzzles me ;-;

77. anonymous

78. anonymous

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

79. anonymous

|dw:1443151869375:dw|

80. anonymous

can my range go lower than a?

81. anonymous

No

82. anonymous

83. anonymous

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

84. anonymous

I mean range:[a, inf)

85. anonymous

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

86. anonymous

instead of an actual number, I assigned a

87. anonymous

Lol

88. anonymous

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

89. anonymous

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

90. anonymous

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

91. anonymous

Gotcha

92. anonymous

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

93. anonymous

Hey I appreciate you helping me :)

94. anonymous

that's why our range starts from 1 to infinity

95. anonymous

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

96. anonymous

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

97. anonymous

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. anonymous

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

99. anonymous

Those I can do fine

100. anonymous

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

101. anonymous

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

102. anonymous

can you write your domain in set-builder notation?

103. anonymous

Mehhh lemme look at some examples and come back to this

104. anonymous

wowwwww lol alright, I need to grab something to eat

105. anonymous

I can't remember how to do it lol

106. anonymous

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

107. anonymous

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

108. anonymous

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

109. anonymous

So it can't be 2 or -2

110. anonymous

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

111. anonymous

correct, so all real except for those two

112. anonymous

How do I do that with notation?

113. anonymous

try

114. anonymous

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

115. anonymous

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

116. anonymous

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

117. anonymous

it is time for you to master it

118. anonymous

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

119. anonymous

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

120. anonymous

Will do

121. anonymous

okay let us attempt to drive this home