Question

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.

Answer 1

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

Answer 2

But the thing is that 5 is included

Answer 3

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.

Answer 4

Same thing will apply if we tried:
\(y=\ln(x-5)\), then 5 is not included.

Answer 5

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.

Answer 6

That makes sense, thank you!

Answer 7

You are welcome