## anonymous one year ago Help with Piecewise?

1. anonymous

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

2. anonymous

ok

3. anonymous

ok

4. anonymous

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

5. anonymous

I have to graph this function.

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

Break the curve?

11. anonymous

The curve of $x^2-3$ looks like this|dw:1438195354274:dw|

12. anonymous

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

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

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

18. anonymous

Yes -3 is y intercept

19. 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

20. anonymous

Ok, so is my y intercept -3 again?

21. anonymous

So its open circle

22. anonymous

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

23. anonymous

Yup

24. anonymous

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

25. 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

26. anonymous

Yes it stops at 4

27. anonymous

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

28. anonymous

Or am I far off? o.o

29. anonymous

Yea you got it

30. anonymous

Yay! Thank you once again! :D

31. anonymous

yw