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

ok

ok

I have to graph this function.

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

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

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

Break the curve?

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

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

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

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

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

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

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

Yes -3 is y intercept

Ok, so is my y intercept -3 again?

So its open circle

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

Yup

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

Yes it stops at 4

Or am I far off? o.o

Yea you got it

Yay! Thank you once again! :D

yw