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

- sloppycanada

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- myininaya

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

- myininaya

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

- sloppycanada

Yes? the last one?

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- myininaya

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

- myininaya

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

- myininaya

which means f(anything in that interval)=2

- myininaya

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

- 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

what?

- myininaya

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

- myininaya

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

- myininaya

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

- sloppycanada

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

- 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

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

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

You lost me.

- myininaya

oh which part?

- myininaya

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

- sloppycanada

which means f(anything in that interval)=2

- sloppycanada

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

- 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

but how did you get 2 from -2?

- myininaya

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

- myininaya

and -2 certainly falls in that interval

- myininaya

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

- sloppycanada

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

- myininaya

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

- 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

does this still make no sense?

- 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

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

- myininaya

to find the output for the function

- sloppycanada

x = -2 and y = 2

- sloppycanada

then what do I do with all these commas?

- myininaya

You don't need to do anything with them

- myininaya

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

- myininaya

but you already found f(-2)

- sloppycanada

okay, then what do I do with it?

- myininaya

what does it refer to?

- myininaya

what third bit?

- myininaya

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

- myininaya

is there another question or something?

- 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

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

- myininaya

we found f(-2)

- sloppycanada

and what is f(-2)? 2?

- myininaya

yes
f(-2)=2

- 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

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

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

- 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

pretty much.

- 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

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

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

- myininaya

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

- 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

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

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

- sloppycanada

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

- myininaya

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

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