## mathmath333 one year ago How to graph this.

1. mathmath333

\large \color{black}{\begin{align} \mid y\mid \geq 1\hspace{.33em}\\~\\ \end{align}}

2. Vocaloid

$\left| y \right| \ge 1$ means that $y \ge 1$ or $y \le -1$ |dw:1434816235241:dw|

3. mathmath333

u mean this one |dw:1434816613473:dw|

4. Vocaloid

yeah, that graph is lot neater, thanks!

5. mathmath333

@Vocaloid but wolfram gave this as the graph |dw:1434816760211:dw|

6. hartnn

1. |y| >= 1 is a one variable inequality. so you'd use a number line. 2. If you want a xy plot, your plot should show regions for all values of y... like if y = -2, would your inequality satisfy ?? is it shown by that plot?

7. hartnn

point 1,2 satisfies your inequality, but the wolf graph says it doesn't :)

8. hartnn

wolf graph is wrong. it plots x =|y| and y =1

9. mathmath333

how can i plot 1 in (1,2) there is no space for x co-ordinate

10. hartnn

it should have plotted x=1 instead of y=1

11. hartnn

|dw:1434817459914:dw|

12. mathmath333

|dw:1434817543444:dw|

13. ganeshie8

how do you sketch y = 1 in 1D, 2D and 3D ?

14. mathmath333

|dw:1434817611958:dw|

15. hartnn

the wolf graph took vertical axis as 'x' ! lol

16. hartnn

if you want a 2D graph for |y|>=1, then the first graph is correct

17. ganeshie8

Haha wolfram is trolling us |dw:1434817710812:dw|

18. hartnn

|y|≥1 means that y≥1 or y≤−1 is absolutely correct

19. mathmath333

but why is that desmos graphing calculator also cannot graph $$|y|\geq 1$$ when i input the syntax.

20. ganeshie8

As the question stands, nobody can stop me from thinking of $$y$$ as distance from origin (polar) ;p |dw:1434817996160:dw|

21. hartnn

"We don't solve complicated single variable equations yet" lol true ganeshie! it depends on how we want to graph...multiple correct answers.

22. hartnn

although the best thing to do here is to plot on the number line!

23. mathmath333

so this below graph correct for $$|y| \geq 1$$ |dw:1434818180900:dw|

24. ganeshie8

yeah some are ridiculous and some are more or less obvious from the context

25. hartnn

yes, it is math. verify by taking different values of y

26. mathmath333

ok thnx

27. Vocaloid

hm, I suppose graphing calculators/graphing software is usually designed to handle x and y together think of it this way: we can graph y = 1, right? it's just a horizontal line through y = 1 y > 1 is just everything shaded above that line.

28. hartnn

y=1 is a point on a number line. y= 1 is a line in xy plot: 2D y=1 is a plane in xyz plot: 3D

29. Vocaloid

^ that, too :)

30. mathmath333

i have checked in geogebra too, it also can't plot $$|y|\geq 1$$

31. ParthKohli

But you can.

32. ganeshie8

try below in geogebra abs(y) >= 1

33. hartnn

so you > desmos/geogebra :P :)

34. ParthKohli

We created Desmos and Geogebra. Humans 1 - 0 Computers

35. mathmath333

tried this "abs(y) >= 1" , nothing happened from geogebra

36. mathmath333

37. ganeshie8

id love to be in a matrix for a change

38. hartnn

|y| >= 1 the first thought that came to mind, all values of y, that are greater than 1, irrespective of the sign of the number....

39. ParthKohli

There's really not much to think about this problem. You just find the set of points with the absolute value of their y-coordinate either 1 or greater than that. So the "base"-set of points would be points with y-coordinate = 1. I just realised that it's exactly what hartnn explained but I don't want to remove this reply so yeah

40. hartnn

|dw:1434819148818:dw|

41. ganeshie8

|dw:1434819259110:dw|

42. ParthKohli

|dw:1434819280155:dw|

43. ganeshie8

|dw:1434819455607:dw|

44. ParthKohli

close enough

45. ganeshie8

your painting looks way prettier than the original smith !

46. ParthKohli

Of course it does - where do you think Smith was inspired from?

47. ganeshie8

|dw:1434819600999:dw|

48. ganeshie8

i remember something like matrix was inspired from Gita

49. ParthKohli

Yes, and that is obviously not true...

50. mathmath333

if i have to plot the graph for this $$y\geq |1|$$ then will it also be same as $$|y|\geq 1$$

51. hartnn

|1| is just 1, right ?

52. mathmath333

but |-1| is also 1

53. hartnn

but your question does not have |-1|

54. hartnn

y >=|1| is same as y>=1 all y values greater than 1. so y will take only positive values, not negative

55. mathmath333

solving $$y>=|1|$$this by algebra will give me this this two inequalities $$y>=1$$ and $$y>=-1$$ right ?

56. ganeshie8

It might help to think of $$|y|$$ as $$|y-0|$$, the distance between a point $$y$$ on number line.and origin $$0$$

57. ganeshie8

$$|1|$$ is same as $$|1-0|$$ the distance between points $$1$$ and $$0$$ on number line

58. hartnn

if there is a variable inside |...| only then it would lead to 2 posibilities if there is a constant, then its a unique value...thats why its called a constant

59. mathmath333

ohk

60. ganeshie8

61. mathmath333

i got a question based on this one If $$|y|\geq 1$$ and $$x=-|a|y$$ , then which one of the following is true? \large \color{black}{\begin{align} a.)\ a-xy<0\hspace{.33em}\\~\\ b.)\ a-xy\geq 0\hspace{.33em}\\~\\ c.)\ a-xy>0\hspace{.33em}\\~\\ d.)\ a-xy\leq 0\hspace{.33em}\\~\\ \end{align}}

62. ParthKohli

Since all of the questions involve the expression $$a - xy$$, let's try to check its nature.$a - xy$$=a - |a|y^2$Now $$y^2 \ge 1$$ so this expression is $$0$$ for $$y = \pm 1$$ and positive $$a$$. As soon as you change $$y$$, it would become negative.

63. hartnn

** a + |a|y^2

64. ParthKohli

Oh wow, skipped that negative sign. =_=

65. ParthKohli

OK thanks, then it should be positive. Looks good.

66. hartnn

|a|y^2 is always positive

67. hartnn

yes, just because |y| >=1 we can say a will be less than or = |a|y^2 numerically and that would make a+ |a|y^2 always positive :)

68. ParthKohli

OK, a better word would be "nonnegative".

69. hartnn

can be 0 ? y can't be 0

70. hartnn

a =0 :P

71. mathmath333

so only options 'b' and 'd' are valid

72. ParthKohli

Ew, what am I even talking about

73. hartnn

b says a-xy is 0 or positive (non-negative) d says a-xy is 0 or negative (non-positive)

74. mathmath333

can $$a$$ be 0

75. hartnn

sure

76. mathmath333

so option be would be correct

77. hartnn

$$\Huge \checkmark$$

78. mathmath333

thnx!

79. hartnn

wlcmx!