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anonymous

  • one year ago

Help with Piecewise?

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  1. anonymous
    • one year ago
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    I'm struggling with triple piecewise functions. So here is an example of one I need help with:

  2. anonymous
    • one year ago
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    ok

  3. anonymous
    • one year ago
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    ok

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

  5. anonymous
    • one year ago
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    I have to graph this function.

  6. anonymous
    • one year ago
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    Btw, the "if-" int the problems were to show the if x is <,>,<= etc.

  7. anonymous
    • one year ago
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    Ok, do them separately, step by step, start with \[f(x) = (x^2-3) \left\{ x<0 \right\}\]

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

  9. anonymous
    • one year ago
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    No, you need to "break" the curve and continue the function, the limits isn't a problem here.

  10. anonymous
    • one year ago
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    Break the curve?

  11. anonymous
    • one year ago
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    The curve of \[x^2-3\] looks like this|dw:1438195354274:dw|

  12. anonymous
    • one year ago
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    But for this part we do it for x<0 so it looks like this |dw:1438195427221:dw|

  13. anonymous
    • one year ago
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    So I need to break the curve? But what can I do to the function to do that?

  14. anonymous
    • one year ago
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    SOrry my replies are a little sometimes because my computer is lagging

  15. anonymous
    • one year ago
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    You gotta imagine that this x^2-3 function is only valid if x is smaller than 0

  16. anonymous
    • one year ago
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    Ok, got it. so would that mean my y intercept is -3?

  17. anonymous
    • one year ago
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    Now we can move on to the 2nd piece \[\frac{ 1 }{ 2 }x-3 \left\{ -0\le x <4 \right\}\]

  18. anonymous
    • one year ago
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    Yes -3 is y intercept

  19. anonymous
    • one year ago
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    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
    • one year ago
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    Ok, so is my y intercept -3 again?

  21. anonymous
    • one year ago
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    So its open circle

  22. anonymous
    • one year ago
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    you remember the y=mx+b? b is the intercept, in this case is -3

  23. anonymous
    • one year ago
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    Yup

  24. anonymous
    • one year ago
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    And now for this one, it goes up to four and stops, right?

  25. anonymous
    • one year ago
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    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
    • one year ago
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    Yes it stops at 4

  27. anonymous
    • one year ago
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    Ok. So all three pieces combined, does it look like this?

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  28. anonymous
    • one year ago
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    Or am I far off? o.o

  29. anonymous
    • one year ago
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    Yea you got it

  30. anonymous
    • one year ago
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    Yay! Thank you once again! :D

  31. anonymous
    • one year ago
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    yw

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