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Ammarah

  • one year ago

Sketch the graph of the piecewise defined function by hand

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  1. Ammarah
    • one year ago
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    |dw:1439747524104:dw|

  2. Ammarah
    • one year ago
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    @ganeshie8 @mathstudent55

  3. Michele_Laino
    • one year ago
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    hint: |dw:1439747762727:dw|

  4. Michele_Laino
    • one year ago
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    here, you have to choose the right pieces from both graphs

  5. Ammarah
    • one year ago
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    oh like if its less than or greater

  6. Ammarah
    • one year ago
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    |dw:1439748014126:dw|

  7. Michele_Laino
    • one year ago
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    hint: |dw:1439748052974:dw|

  8. Michele_Laino
    • one year ago
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    what is the domain of that second function?

  9. Ammarah
    • one year ago
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    ?

  10. Michele_Laino
    • one year ago
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    please wait a moment

  11. Michele_Laino
    • one year ago
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    for example I consider the subsequent function: f(x)= sqrt(4-x) Now the radical exists, if and only if the subsequent condition holds: \[4 - x \geqslant 0 \Rightarrow x \leqslant 4\] am I right?

  12. Ammarah
    • one year ago
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    yes

  13. Michele_Laino
    • one year ago
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    so that part of function is defined inside this interval of the real line: \[0 \leqslant x \leqslant 4\]

  14. Michele_Laino
    • one year ago
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    since, from your definition sqrt(4-x) is given for all x such that they are greater or equal to zero

  15. Michele_Laino
    • one year ago
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    now, please do the same with the other part of your function, namely f(x)=sqrt(4+x)

  16. Michele_Laino
    • one year ago
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    hint: from your definition we have x<0, furthermore, the radical exists if and only if \[4 + x \geqslant 0\] so, what do you get?

  17. Michele_Laino
    • one year ago
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    please note that in order to draw the graph of your function, we need to know its domain

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