## 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.

1. 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|

2. clara1223

But the thing is that 5 is included

3. 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.

4. SolomonZelman

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

5. 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.

6. clara1223

That makes sense, thank you!

7. SolomonZelman

You are welcome