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clara1223
 one year ago
1) Is it possible to have a function f defined on [ 2 , 4 ] and meets the given conditions?
f is continuous on [ 2 , 4 ), minimum value f(4)=2, and no maximum value.
2) Is it possible to have a function f defined on [ 4 , 5 ] and meets the given conditions?
f is continuous on [ 4 , 5 ], takes on no rational values.
3) Is it possible to have a function f defined on [ 2 , 5 ] and meets the given conditions?
f is continuous on [ 2 ,5 ] and the range of f is an unbounded interval.
clara1223
 one year ago
1) Is it possible to have a function f defined on [ 2 , 4 ] and meets the given conditions? f is continuous on [ 2 , 4 ), minimum value f(4)=2, and no maximum value. 2) Is it possible to have a function f defined on [ 4 , 5 ] and meets the given conditions? f is continuous on [ 4 , 5 ], takes on no rational values. 3) Is it possible to have a function f defined on [ 2 , 5 ] and meets the given conditions? f is continuous on [ 2 ,5 ] and the range of f is an unbounded interval.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i am thinking of a counter example for the first one, but i can't seem to come up with one i bet you can come up with and example for #2, think of a constant function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0#3 contradicts whatever theorem it is that says a continuous function on a closed interval has a max and a min

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i bet @Zarkon can come up with an example for the first one

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0So far we have that for 2 it is possible, but for 3 it isn't possible?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0who said art was dead?

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0that makes a lot of sense!

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0so 1 is possible, 2 is possible, but 3 isn't possible. correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i was thinking of \[\frac{1}{4x},2\] or something similar dw:1441940311469:dwdw:1441940327769:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah did you come up with an example for #2?

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441940405617:dw

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0I didn't think it mattered, as long as x=4 and x=5 were defined

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it matters a great deal for example, if your function is \[f(x)=3\]then it is rational on that inteval

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0so what y value would satisfy this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0btw defined on \([4,5]\) means defined for all \(x\) in the interval \(4\leq x\leq 5\)not just at the endpoints

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why doesn't \[f(x)=3\]work?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x)=3\]is an example of a function that is continuous and defined on any interval you like, including \([4,5]\) but it s not always irrational on that interval because... because it is always rational on the interval on account of 3 is a rational number

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so that is NOT an example, but you can modify it so that it is an example of a function that is never rational just don't pick 3

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0oh, so would y=sqrt(2) work? that is an irrational number
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