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sloppycanada

  • one year ago

How do I solve piecewise functions? I cannot tell you how many times I have stared at my notes and done the practice. https://gyazo.com/8740807019fb8b146a7ec27a3565554e

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  1. myininaya
    • one year ago
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    f(-2) can be evaluated by the piece that includes x=-2

  2. myininaya
    • one year ago
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    is -2 in the set of numbers that is described by x>=0? by x<-3? or by -3<=x<0?

  3. sloppycanada
    • one year ago
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    Yes? the last one?

  4. myininaya
    • one year ago
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    yes the last one -2 is between -3 and 0

  5. myininaya
    • one year ago
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    so you use f(x)=2 since x is between -3 and 0

  6. myininaya
    • one year ago
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    which means f(anything in that interval)=2

  7. myininaya
    • one year ago
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    f(-1)=2 f(-1/2)=2 f(-2.534)=2

  8. sloppycanada
    • one year ago
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    so that means my answer is 2? So okay, the way I see is if the f(-2) or whatever number it is, happens to be in the set of functions, then the answer to f(x) is the opposite?

  9. myininaya
    • one year ago
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    what?

  10. myininaya
    • one year ago
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    I used f(x)=2 since x is between -3 and 0

  11. myininaya
    • one year ago
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    if it said evaluate f(-5) I would have used f(x)=|x+3| since x is less than -3

  12. myininaya
    • one year ago
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    f(-5)=|-5+3|=|-2|=2

  13. sloppycanada
    • one year ago
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    so it has to fit in the thing? i'm confused now.

  14. myininaya
    • one year ago
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    remember the first thing we looked at is what set of x values our x was included in then we used the corresponding piece

  15. myininaya
    • one year ago
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    another example if we wanted to evaluated f(-10) -10 is less than -3 and our function says use f(x)=|x+3| if x is less than -3 so f(-10)=|-10+3|=-7|=7

  16. myininaya
    • one year ago
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    another example if we wanted to evaluate f(20) well 20 is greater than 0 and our function says to use f(x)=x if x greater than or equal to 0 so f(20)=20

  17. sloppycanada
    • one year ago
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    You lost me.

  18. myininaya
    • one year ago
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    oh which part?

  19. myininaya
    • one year ago
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    f(-10) or f(20) or what?

  20. sloppycanada
    • one year ago
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    which means f(anything in that interval)=2

  21. sloppycanada
    • one year ago
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    Like I said, I really don't get these piecewise functions..

  22. myininaya
    • one year ago
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    before I said that I said this "so you use f(x)=2 since x is between -3 and 0" the interval being [-3,0) actually since it says to include -3 f(anything in that interval)=2 means any x value in [-3,0) will give us the output 2 when put into our function examples f(-3)=2 f(-2.9999)=2 f(-2.5)=2 f(-2)=2 f(-1.99)=2 f(-1.5)=2 f(-1/2)=2 f(-1/5)=2

  23. sloppycanada
    • one year ago
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    but how did you get 2 from -2?

  24. myininaya
    • one year ago
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    Your function says to use f(x)=2 if -3<=x<0

  25. myininaya
    • one year ago
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    and -2 certainly falls in that interval

  26. myininaya
    • one year ago
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    f(-2)=2 since -3<=-2<0

  27. sloppycanada
    • one year ago
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    Okay, so that little comma thing is like "if this answer is right, use "2" for x "

  28. myininaya
    • one year ago
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    no x is -2 in your problem f(x) or y is 2 for your problem

  29. myininaya
    • one year ago
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    if it did say evaluate f(2) then you would look at the inequalities (or intervals whatever you want to call them) and see which one it satisfies 2>=0 so we use f(x)=x since x>=0 for this example so f(2)=2

  30. myininaya
    • one year ago
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    does this still make no sense?

  31. myininaya
    • one year ago
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    your function says: if x>=0 then use f(x)=x if x<-3 then use f(x)=|x+3| if -3<=x<0 then use f(x)=2

  32. myininaya
    • one year ago
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    find which if part is true for your x then use function that corresponds to that inequality

  33. myininaya
    • one year ago
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    to find the output for the function

  34. sloppycanada
    • one year ago
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    x = -2 and y = 2

  35. sloppycanada
    • one year ago
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    then what do I do with all these commas?

  36. myininaya
    • one year ago
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    You don't need to do anything with them

  37. myininaya
    • one year ago
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    if you want you can replace them with the word if if you prefer that

  38. myininaya
    • one year ago
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    but you already found f(-2)

  39. sloppycanada
    • one year ago
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    okay, then what do I do with it?

  40. myininaya
    • one year ago
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    what does it refer to?

  41. myininaya
    • one year ago
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    what third bit?

  42. myininaya
    • one year ago
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    I'm absolutely lost on what we are talking about now

  43. myininaya
    • one year ago
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    is there another question or something?

  44. myininaya
    • one year ago
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    The only question I see is find f(-2) and we done that I don't see a third or even a second question on the picture you posted

  45. sloppycanada
    • one year ago
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    but what did we find? I'm confused on what we actually found.

  46. myininaya
    • one year ago
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    we found f(-2)

  47. sloppycanada
    • one year ago
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    and what is f(-2)? 2?

  48. myininaya
    • one year ago
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    yes f(-2)=2

  49. myininaya
    • one year ago
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    remember if we have -3<=x<0 then we use f(x)=2 and we had x=-2 was included in -3<=x<0 so we used f(x)=2 to find f(-2)

  50. myininaya
    • one year ago
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    insert any number from the inequality -3<=x<0 into f(x) and you get the output 2 insert any number from the inequality x>=0 into f(x) you get the output x insert any number from the inequality x<-3 into f(x) you get the output |x+3|

  51. sloppycanada
    • one year ago
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    so my answer to this problem is 2, which I think is C?

  52. myininaya
    • one year ago
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    So I guess you are asking me this question for the 4th time because you still don't understand why f(-2)=2?

  53. sloppycanada
    • one year ago
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    pretty much.

  54. myininaya
    • one year ago
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    Ok do you understand the below? \[f(x)=x \text{ if } x \ge 0 \\ f(x)=|x+3| \text{ if } x<-3 \\ f(x)=2 \text{ if } -3 \le x <0 \]

  55. myininaya
    • one year ago
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    we plugged in -2 we are looking for f(-2) we replaced x with -2 replace all the x's with -2 \[f(-2)=-2 \text{ if } -2 \ge 0 \\ f(-2)=|-2+3| \text{ if } -2<-3 \\ f(-2)=2 \text{ if } -3 \le x <0\] the only line that is true here is the last line do you see why?

  56. myininaya
    • one year ago
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    *\[f(-2)=-2 \text{ if } -2 \ge 0 \\ f(-2)=|-2+3| \text{ if } -2<-3 \\ f(-2)=2 \text{ if } -3 \le -2 <0\]*

  57. myininaya
    • one year ago
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    the only line that is true here is the last line do you see why?

  58. myininaya
    • one year ago
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    the last line is the only line that is true since: \[f(-2)=-2 \text{ if } -2 \cancel{\ge} 0 \\ f(-2)=|-2+3| \text{ if } -2\cancel{<}-3 \\ f(-2)=2 \text{ if } -3 \le -2 <0\]

  59. sloppycanada
    • one year ago
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    yes, i get why we have 2. kinda. but i'm not sure what to do with it. Is it the answer to the problem?

  60. myininaya
    • one year ago
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    the last line says f(-2)=2 ...

  61. sloppycanada
    • one year ago
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    which makes 2 our answer. so the answer to the original problem is 2.

  62. myininaya
    • one year ago
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    did you want to try more examples? if so see if you can find f(-100)

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