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clara1223

  • one year ago

State whether it is possible to have a function f defined on the indicated interval and meets the given conditions: f is defined on [2, 5]; f is continuous on [2, 5] and the range of f is an unbounded interval.

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  1. SolomonZelman
    • one year ago
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    My first thought on this is that if your function was continuous on the interval [2,5), then we can make a function with an asymptote at x=5 |dw:1441663465248:dw|

  2. clara1223
    • one year ago
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    But the thing is that 5 is included

  3. SolomonZelman
    • one year ago
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    Yes, I know. And this is why I am saying that if there is an asymptote at x=5, then the functin is not defined at 5, so value of 5 will not be included. (Similarly, we can't make a function with an asymptote at x=2). Therefore a case of an asymptote won't work.

  4. SolomonZelman
    • one year ago
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    Same thing will apply if we tried: \(y=\ln(x-5)\), then 5 is not included.

  5. SolomonZelman
    • one year ago
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    So I would say that for a function to be continuous on [a,b], and to have an unbound range on this very interval is not a possibility.

  6. clara1223
    • one year ago
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    That makes sense, thank you!

  7. SolomonZelman
    • one year ago
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    You are welcome

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