Help with Piecewise?

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Help with Piecewise?

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I'm struggling with triple piecewise functions. So here is an example of one I need help with:
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\[f(x)=\left\{ x^2-3 \right\} (if -x<0)\] \[\frac{ 1 }{ 2 }x-3(if-0 \le x<4)\] \[(x-4)^2-1 (if-x \ge 4)\]
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 \[f(x) = (x^2-3) \left\{ x<0 \right\}\]
That's where I am a little confused to be honest. Because doesn't that give x a limit into negative infinite?
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
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
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?
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
Yes it stops at 4
Ok. So all three pieces combined, does it look like this?
1 Attachment
Or am I far off? o.o
Yea you got it
Yay! Thank you once again! :D
yw

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