## anonymous one year ago describe how to graph a piecewise-defined function.

1. anonymous

@campbell_st

2. e.mccormick

Well.... do you know how to graph a function?

3. anonymous

explain using graphs and words

4. e.mccormick

Well, if you know how to do a graph, a piecewise one is just graphing the pieces.

5. anonymous

no i don't

6. anonymous

i am a beginner

7. e.mccormick

Hmmm... well, do yo know how say $$x^2$$ is a parabola on a graph?

8. anonymous

|dw:1440462346722:dw|

9. campbell_st

well a parking station is an example of a piece wise graph or the cost of posting items there are limits for different conditions... e.g Parking fees free 0 < time <= 1 hour $1 1 < time < = 2 hours$3 2 < time <- 4 hours $10 time > 4 hours |dw:1440462065082:dw| 10. anonymous ok 11. anonymous that is understandable 12. e.mccormick Sortof... And how y=x is just a line at a 45 degree angle that passes through 0. A piecewise is defined by some rules, so if I say: $$x^2 \text{ for } x \le 0$$ $$x \text{ for } x > 0$$ Then it is just both the parabola and the line and where they meet: |dw:1440462351205:dw| 13. campbell_st so in extending this idea you can have |dw:1440462312993:dw| 14. e.mccormick Here is better view of my graph: https://www.desmos.com/calculator/qduk9fxrbk 15. anonymous thanks 16. e.mccormick x^3! That is way up there. LOL.... but as campbell_st is pointing out, it also means they do not need to touch. https://www.desmos.com/calculator/6hl6ntxydl That is a graph of his last one. 17. anonymous ohh 18. e.mccormick If you look at that graph, you will see the x^3 part does not start until y=64! So between y= a little less than 16 to y=63.999999999999 etc. there is just no y values at all. 19. anonymous @e.mccormick 20. anonymous |dw:1440463601392:dw| 21. anonymous so are those related to the car parking example 22. anonymous @Nnesha 23. anonymous are those related to the car parking example 24. anonymous |dw:1440463703158:dw| 25. anonymous @e.mccormick 26. e.mccormick No, he did a different example to show some options. That is why I did the graph of that one on desmos as the last graph I did. 27. anonymous what are the intervals of the park station example 28. anonymous @e.mccormick 29. anonymous |dw:1440464506395:dw| 30. anonymous what are the intervals of the graph 31. e.mccormick That part: Parking fees free 0 < time <= 1 hour$1 1 < time < = 2 hours $3 2 < time <- 4 hours$10 time > 4 hours

32. anonymous

yes

33. e.mccormick

I am saying that those are the intervals he graphed.

34. anonymous

ok

35. anonymous

|dw:1440465233293:dw| what is that arrow?

36. anonymous

what is that arrow

37. anonymous

@e.mccormick

38. e.mccormick

It keeps going.

39. anonymous

|dw:1440465386630:dw|

40. anonymous

i want the intervals to be written like that

41. e.mccormick

$10 time > 4 hours The > means, "From this point and one second more on to it stays there forever, it is$10." So on the graph you use an arrow.

42. e.mccormick

that is the other one I graphed.

43. anonymous

how do we identify the intervals

44. anonymous

what is the domain for the example

45. anonymous

|dw:1440465552670:dw|

46. anonymous

what is the domain?

47. anonymous

domain and range?

48. e.mccormick

The domain is the valid set of input variables. So, what is the minimum ammount of time you can park a car?

49. anonymous

1 hr

50. anonymous

yup it is 1hr

51. anonymous

for 1 hr it is free

52. e.mccormick

Nope. It has 0 there... so if a person pulls in, urns arounf, and leaves they have parked for 0 time.

53. anonymous

so the domain is x=0

54. e.mccormick

Starts at 0. It ends at the maximum time you can park.

55. anonymous

x=infinite

56. e.mccormick

fyi: It is normally done with a brace: $$f(x)\begin{cases} 2x+3 & \text{, } x<0 \\ x^2 & \text{, } x\le x < 4 \\ x^3 & \text{, } x\ge 4 \end{cases}$$

57. anonymous

can you write the steps of graphing the piece wise function?

58. e.mccormick

So the domain is from 0 to infinity.

59. anonymous

so the domain is the braces one?

60. e.mccormick

The steps are the same as any graph, but there are restrictions on how long you need to draw each part. The domain can be written several ways. You might use the union/intersection signs (cup and cap), or you might use interval notation or you might write it out long hand... depends on what the instructor wants.

61. anonymous

the question is "In your own words, describe how to graph a piecewise-defined function."

62. anonymous

so plzz help

63. e.mccormick

Like I said, you graph each part, but you need to keep track of where you start and stop.

64. e.mccormick
65. anonymous

but, the braces one is the domain right?

66. e.mccormick

Yes. So $$[0, \infty)$$ for domain. The range would be set in that example. There are only 4 y values.

67. anonymous

ok

68. anonymous

(0,1,3,10)

69. anonymous

that is the range right?

70. anonymous

set of y values

71. anonymous

can you do the other problem for me?

72. anonymous

I tagged you

73. e.mccormick

That is the correct range.