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Question

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anonymous · Answer

I gave you a medal! I'll watch this, this is quite interesting, OK?

anonymous · Answer

Okay a piece-wise function is a function that has two different parts to it.

solomonzelman · Answer

Sure @Rahcel_97! I don't mind and don't think wio does either!

anonymous · Answer

TNX! OK! Go on please!

anonymous · Answer

$$
f(x) = \begin{cases}
2x-2&x>2\
x&x\leq 2
\end{cases}
$$

solomonzelman · Answer

piece wise?

anonymous · Answer

Have you seen these before?

solomonzelman · Answer

If you remove f(x) and the parenthesis, you will then turn Calculus 1 into Algebra 1.

solomonzelman · Answer

Not as a function.

anonymous · Answer

Okay.  Well do you know what $f(0)$ would be in this function?

solomonzelman · Answer

Rachel, medal, to wio, please!

solomonzelman · Answer

0 <2
0 =<2
?

solomonzelman · Answer

No -2<2
    0=<2

anonymous · Answer

Yes, that means you want to use the bottom part. So $f(x)=x$ and  $f(0) =0$

solomonzelman · Answer

So my 2nd answer is right?

anonymous · Answer

I'm not sure what you were doing.

anonymous · Answer

But in the end $f(0)=0$.

Do you know what $f(1)$ would be?

solomonzelman · Answer

I plugged -2 for x in a first line/equation
and 0 for x in a 2hd line/equation

solomonzelman · Answer

1
and f(100)=100
Right?

anonymous · Answer

Well,  $100>2$

anonymous · Answer

So you would have to use the top one.

anonymous · Answer

$$
f(100) = 2(100)-2 = 200-2=198
$$

solomonzelman · Answer

I see and for 1 it is -1

solomonzelman · Answer

I think I get this!

anonymous · Answer

Well $f(1)=1$

solomonzelman · Answer

I though I should use the top equation?

anonymous · Answer

Well $1\leq 2$ so you use the bottom one.

solomonzelman · Answer

Oh, for top equation it is 0
so we are using the bottom one and get 1, correct?

solomonzelman · Answer

I get it!

solomonzelman · Answer

You deserve 100 medals for this!

anonymous · Answer

Okay so with this piece wise function, notice that at $2$ is where it changes up.

solomonzelman · Answer

Why?

anonymous · Answer

Because $x>2$ and $x\leq 2$, so at $2$ you use the bottom one, but it is where they switch off.

solomonzelman · Answer

I see, use the bottom one b/c it is the one that is true, b/c 2<2 is false...!

anonymous · Answer

Anyway, if we look at $x\to 3$  then we would just use the top one for the limit.  If we look at $x\to 1$ we use the bottom one for the limit.

For $x\to 2$ we must use both.

solomonzelman · Answer

|dw:1381815976888:dw|

Just recalling.