anonymous
  • anonymous
Help with Piecewise?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
I'm struggling with triple piecewise functions. So here is an example of one I need help with:
anonymous
  • anonymous
ok
anonymous
  • anonymous
ok

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anonymous
  • 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
  • anonymous
I have to graph this function.
anonymous
  • anonymous
Btw, the "if-" int the problems were to show the if x is <,>,<= etc.
anonymous
  • anonymous
Ok, do them separately, step by step, start with \[f(x) = (x^2-3) \left\{ x<0 \right\}\]
anonymous
  • anonymous
That's where I am a little confused to be honest. Because doesn't that give x a limit into negative infinite?
anonymous
  • anonymous
No, you need to "break" the curve and continue the function, the limits isn't a problem here.
anonymous
  • anonymous
Break the curve?
anonymous
  • anonymous
The curve of \[x^2-3\] looks like this|dw:1438195354274:dw|
anonymous
  • anonymous
But for this part we do it for x<0 so it looks like this |dw:1438195427221:dw|
anonymous
  • anonymous
So I need to break the curve? But what can I do to the function to do that?
anonymous
  • anonymous
SOrry my replies are a little sometimes because my computer is lagging
anonymous
  • anonymous
You gotta imagine that this x^2-3 function is only valid if x is smaller than 0
anonymous
  • anonymous
Ok, got it. so would that mean my y intercept is -3?
anonymous
  • anonymous
Now we can move on to the 2nd piece \[\frac{ 1 }{ 2 }x-3 \left\{ -0\le x <4 \right\}\]
anonymous
  • anonymous
Yes -3 is y intercept
anonymous
  • 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
  • anonymous
Ok, so is my y intercept -3 again?
anonymous
  • anonymous
So its open circle
anonymous
  • anonymous
you remember the y=mx+b? b is the intercept, in this case is -3
anonymous
  • anonymous
Yup
anonymous
  • anonymous
And now for this one, it goes up to four and stops, right?
anonymous
  • 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
  • anonymous
Yes it stops at 4
anonymous
  • anonymous
Ok. So all three pieces combined, does it look like this?
1 Attachment
anonymous
  • anonymous
Or am I far off? o.o
anonymous
  • anonymous
Yea you got it
anonymous
  • anonymous
Yay! Thank you once again! :D
anonymous
  • anonymous
yw

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