## 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

1. myininaya

f(-2) can be evaluated by the piece that includes x=-2

2. myininaya

is -2 in the set of numbers that is described by x>=0? by x<-3? or by -3<=x<0?

Yes? the last one?

4. myininaya

yes the last one -2 is between -3 and 0

5. myininaya

so you use f(x)=2 since x is between -3 and 0

6. myininaya

which means f(anything in that interval)=2

7. myininaya

f(-1)=2 f(-1/2)=2 f(-2.534)=2

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

what?

10. myininaya

I used f(x)=2 since x is between -3 and 0

11. myininaya

if it said evaluate f(-5) I would have used f(x)=|x+3| since x is less than -3

12. myininaya

f(-5)=|-5+3|=|-2|=2

so it has to fit in the thing? i'm confused now.

14. myininaya

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

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

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

You lost me.

18. myininaya

oh which part?

19. myininaya

f(-10) or f(20) or what?

which means f(anything in that interval)=2

Like I said, I really don't get these piecewise functions..

22. myininaya

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

but how did you get 2 from -2?

24. myininaya

Your function says to use f(x)=2 if -3<=x<0

25. myininaya

and -2 certainly falls in that interval

26. myininaya

f(-2)=2 since -3<=-2<0

Okay, so that little comma thing is like "if this answer is right, use "2" for x "

28. myininaya

no x is -2 in your problem f(x) or y is 2 for your problem

29. myininaya

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

does this still make no sense?

31. myininaya

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

find which if part is true for your x then use function that corresponds to that inequality

33. myininaya

to find the output for the function

x = -2 and y = 2

then what do I do with all these commas?

36. myininaya

You don't need to do anything with them

37. myininaya

if you want you can replace them with the word if if you prefer that

38. myininaya

okay, then what do I do with it?

40. myininaya

what does it refer to?

41. myininaya

what third bit?

42. myininaya

I'm absolutely lost on what we are talking about now

43. myininaya

is there another question or something?

44. myininaya

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

but what did we find? I'm confused on what we actually found.

46. myininaya

we found f(-2)

and what is f(-2)? 2?

48. myininaya

yes f(-2)=2

49. myininaya

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

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|

so my answer to this problem is 2, which I think is C?

52. myininaya

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

pretty much.

54. myininaya

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

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

*$f(-2)=-2 \text{ if } -2 \ge 0 \\ f(-2)=|-2+3| \text{ if } -2<-3 \\ f(-2)=2 \text{ if } -3 \le -2 <0$*

57. myininaya

the only line that is true here is the last line do you see why?

58. myininaya

the last line is the only line that is true since: $f(-2)=-2 \text{ if } -2 \cancel{\ge} 0 \\ f(-2)=|-2+3| \text{ if } -2\cancel{<}-3 \\ f(-2)=2 \text{ if } -3 \le -2 <0$

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

the last line says f(-2)=2 ...

which makes 2 our answer. so the answer to the original problem is 2.

62. myininaya

did you want to try more examples? if so see if you can find f(-100)