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

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?

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

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

which means f(anything in that interval)=2

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

what?

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

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

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

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

You lost me.

oh which part?

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..

but how did you get 2 from -2?

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

and -2 certainly falls in that interval

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

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

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

does this still make no sense?

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

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

to find the output for the function

x = -2 and y = 2

then what do I do with all these commas?

You don't need to do anything with them

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

but you already found f(-2)

okay, then what do I do with it?

what does it refer to?

what third bit?

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

is there another question or something?

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

we found f(-2)

and what is f(-2)? 2?

yes
f(-2)=2

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

pretty much.

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

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

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

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