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anonymous

  • one year ago

What is the discontinuity and zero of the function f(x) = the quantity of 2 x squared plus 5 x minus 12, all over x plus 4?

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  1. amilapsn
    • one year ago
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    A function is said to be discontinuous at a point if we can't draw the graph without lifting our pen at that point.

  2. MrNood
    • one year ago
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    in a function like this the discontinuity will occur where the denominator = 0 \[f(x) = \frac{ 5x ^{2}+5x-12 }{ x+4 }\] If you set f(x) = 0 then you are left with just the quadratic to solve

  3. MrNood
    • one year ago
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    CORRECTION - should be 2x^2 above BUT 2x^2+5x-12 = (x+4)(2x-3) so the equation becomes y=2x-3 which has no discontinuity. Have I interpreted the equation correctly?

  4. sweetburger
    • one year ago
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    Isnt this still a discontinuous function?

  5. MrNood
    • one year ago
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    if the equation is \[f(x) = \frac{ (2x)^{2}+5x-12 }{ (x+4) }\] THEN my comments above are true because(2x)^2 = 4x^2 @sweetburger It looks like it should be - but because the denominator cancels with the factor in the numerator it becomes a continulas straight line

  6. sweetburger
    • one year ago
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    Yea I realized when I graphed it that you are indeed correct.

  7. sweetburger
    • one year ago
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    Wait actually according to my graphing calculator there is a large gap in the graph

  8. sweetburger
    • one year ago
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    ill screenshot it one second

  9. MrNood
    • one year ago
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  10. MrNood
    • one year ago
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    the question asks for the 'zero' but in most cases there are 2 zeroes I think I may have misinterpreted the way the question is written - or it is written incorrectly.

  11. sweetburger
    • one year ago
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    welp i was doing 5x^2 instead of 2x^2 my bad

  12. MrNood
    • one year ago
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    soz - that was my initial typo but there are 2 zeroes in other values for ax^2

  13. sweetburger
    • one year ago
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    Yea, I see the 2 zeroe values with the correct equation. I understand where your answer came from now.

  14. MrNood
    • one year ago
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    no - my point is that if the equation is as I wrote then there is ONE zero (as it is a straight line - but NO discontinuity If the equation is other, then there are 2 zeroes , and a discontinuity @ x=-4

  15. sweetburger
    • one year ago
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    I mean I see where your coming from as the x+4 cancel out and your left with a straight line with no discontinuities represented by y=2x+3. At least i think this is what your were saying.

  16. MrNood
    • one year ago
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    yes - that's it I still think there is an error with the question, or with my interpretation. But the asker is offline so I'll wait foe his reply.

  17. sweetburger
    • one year ago
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    Yea the question seems to be misworded in some way or the asker typed it in wrong.

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