sloppycanada
  • sloppycanada
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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myininaya
  • myininaya
f(-2) can be evaluated by the piece that includes x=-2
myininaya
  • myininaya
is -2 in the set of numbers that is described by x>=0? by x<-3? or by -3<=x<0?
sloppycanada
  • sloppycanada
Yes? the last one?

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myininaya
  • myininaya
yes the last one -2 is between -3 and 0
myininaya
  • myininaya
so you use f(x)=2 since x is between -3 and 0
myininaya
  • myininaya
which means f(anything in that interval)=2
myininaya
  • myininaya
f(-1)=2 f(-1/2)=2 f(-2.534)=2
sloppycanada
  • sloppycanada
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?
myininaya
  • myininaya
what?
myininaya
  • myininaya
I used f(x)=2 since x is between -3 and 0
myininaya
  • myininaya
if it said evaluate f(-5) I would have used f(x)=|x+3| since x is less than -3
myininaya
  • myininaya
f(-5)=|-5+3|=|-2|=2
sloppycanada
  • sloppycanada
so it has to fit in the thing? i'm confused now.
myininaya
  • 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
myininaya
  • 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
myininaya
  • 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
sloppycanada
  • sloppycanada
You lost me.
myininaya
  • myininaya
oh which part?
myininaya
  • myininaya
f(-10) or f(20) or what?
sloppycanada
  • sloppycanada
which means f(anything in that interval)=2
sloppycanada
  • sloppycanada
Like I said, I really don't get these piecewise functions..
myininaya
  • 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
sloppycanada
  • sloppycanada
but how did you get 2 from -2?
myininaya
  • myininaya
Your function says to use f(x)=2 if -3<=x<0
myininaya
  • myininaya
and -2 certainly falls in that interval
myininaya
  • myininaya
f(-2)=2 since -3<=-2<0
sloppycanada
  • sloppycanada
Okay, so that little comma thing is like "if this answer is right, use "2" for x "
myininaya
  • myininaya
no x is -2 in your problem f(x) or y is 2 for your problem
myininaya
  • 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
myininaya
  • myininaya
does this still make no sense?
myininaya
  • 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
myininaya
  • myininaya
find which if part is true for your x then use function that corresponds to that inequality
myininaya
  • myininaya
to find the output for the function
sloppycanada
  • sloppycanada
x = -2 and y = 2
sloppycanada
  • sloppycanada
then what do I do with all these commas?
myininaya
  • myininaya
You don't need to do anything with them
myininaya
  • myininaya
if you want you can replace them with the word if if you prefer that
myininaya
  • myininaya
but you already found f(-2)
sloppycanada
  • sloppycanada
okay, then what do I do with it?
myininaya
  • myininaya
what does it refer to?
myininaya
  • myininaya
what third bit?
myininaya
  • myininaya
I'm absolutely lost on what we are talking about now
myininaya
  • myininaya
is there another question or something?
myininaya
  • 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
sloppycanada
  • sloppycanada
but what did we find? I'm confused on what we actually found.
myininaya
  • myininaya
we found f(-2)
sloppycanada
  • sloppycanada
and what is f(-2)? 2?
myininaya
  • myininaya
yes f(-2)=2
myininaya
  • 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)
myininaya
  • 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|
sloppycanada
  • sloppycanada
so my answer to this problem is 2, which I think is C?
myininaya
  • myininaya
So I guess you are asking me this question for the 4th time because you still don't understand why f(-2)=2?
sloppycanada
  • sloppycanada
pretty much.
myininaya
  • myininaya
Ok do you understand the below? \[f(x)=x \text{ if } x \ge 0 \\ f(x)=|x+3| \text{ if } x<-3 \\ f(x)=2 \text{ if } -3 \le x <0 \]
myininaya
  • 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?
myininaya
  • myininaya
*\[f(-2)=-2 \text{ if } -2 \ge 0 \\ f(-2)=|-2+3| \text{ if } -2<-3 \\ f(-2)=2 \text{ if } -3 \le -2 <0\]*
myininaya
  • myininaya
the only line that is true here is the last line do you see why?
myininaya
  • myininaya
the last line is the only line that is true since: \[f(-2)=-2 \text{ if } -2 \cancel{\ge} 0 \\ f(-2)=|-2+3| \text{ if } -2\cancel{<}-3 \\ f(-2)=2 \text{ if } -3 \le -2 <0\]
sloppycanada
  • sloppycanada
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?
myininaya
  • myininaya
the last line says f(-2)=2 ...
sloppycanada
  • sloppycanada
which makes 2 our answer. so the answer to the original problem is 2.
myininaya
  • myininaya
did you want to try more examples? if so see if you can find f(-100)

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