clara1223
  • clara1223
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.
Mathematics
chestercat
  • chestercat
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SolomonZelman
  • SolomonZelman
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|
clara1223
  • clara1223
But the thing is that 5 is included
SolomonZelman
  • SolomonZelman
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.

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SolomonZelman
  • SolomonZelman
Same thing will apply if we tried: \(y=\ln(x-5)\), then 5 is not included.
SolomonZelman
  • SolomonZelman
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.
clara1223
  • clara1223
That makes sense, thank you!
SolomonZelman
  • SolomonZelman
You are welcome

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