Help with Piecewise?

- anonymous

Help with Piecewise?

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- schrodinger

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- anonymous

I'm struggling with triple piecewise functions. So here is an example of one I need help with:

- anonymous

ok

- anonymous

ok

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## More answers

- anonymous

\[f(x)=\left\{ x^2-3 \right\} (if -x<0)\]
\[\frac{ 1 }{ 2 }x-3(if-0 \le x<4)\]
\[(x-4)^2-1 (if-x \ge 4)\]

- anonymous

I have to graph this function.

- anonymous

Btw, the "if-" int the problems were to show the if x is <,>,<= etc.

- anonymous

Ok, do them separately, step by step, start with
\[f(x) = (x^2-3) \left\{ x<0 \right\}\]

- anonymous

That's where I am a little confused to be honest. Because doesn't that give x a limit into negative infinite?

- anonymous

No, you need to "break" the curve and continue the function, the limits isn't a problem here.

- anonymous

Break the curve?

- anonymous

The curve of
\[x^2-3\]
looks like this|dw:1438195354274:dw|

- anonymous

But for this part we do it for x<0 so it looks like this
|dw:1438195427221:dw|

- anonymous

So I need to break the curve? But what can I do to the function to do that?

- anonymous

SOrry my replies are a little sometimes because my computer is lagging

- anonymous

You gotta imagine that this x^2-3 function is only valid if x is smaller than 0

- anonymous

Ok, got it. so would that mean my y intercept is -3?

- anonymous

Now we can move on to the 2nd piece
\[\frac{ 1 }{ 2 }x-3 \left\{ -0\le x <4 \right\}\]

- anonymous

Yes -3 is y intercept

- anonymous

And also because the condition of the function is x<0, it doesnt include 0 so the ending at the y intercept looks like this:|dw:1438195804679:dw|
Notice its a hollow dot, which means it does not include x=0

- anonymous

Ok, so is my y intercept -3 again?

- anonymous

So its open circle

- anonymous

you remember the y=mx+b?
b is the intercept, in this case is -3

- anonymous

Yup

- anonymous

And now for this one, it goes up to four and stops, right?

- anonymous

now its \[\frac{ 1 }{ 2 }x-3\]
this is a straight line and also the function includes 0.
The y-intercept of this function is also at -3

- anonymous

Yes it stops at 4

- anonymous

Ok. So all three pieces combined, does it look like this?

##### 1 Attachment

- anonymous

Or am I far off? o.o

- anonymous

Yea you got it

- anonymous

Yay! Thank you once again! :D

- anonymous

yw

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