Calculus determining a function with a limit

[HelpIsWanted]

Let a function, f have the domain of real numbers

What is a function with the points (-1,0) and (1,2) but has a limit as x approaches infinity for the sin of that function?

 

[Dr.Peterson]

Is that exactly how the problem was given to you?

It sounds like it means something like this:

Let f be a function on the real numbers, such that [MATH]f(-1) = 0[/MATH], [MATH]f(2) = 2[/MATH], and [MATH]\lim_{x\to \infty}\sin(f(x))[/MATH] exists.​

Is that correct?

 

[lev888]

If sin(f(x)) has a limit, what can we say about the value of f(x) as x approaches infinity?

 

[HelpIsWanted]

Is that exactly how the problem was given to you?

It sounds like it means something like this:

Let f be a function on the real numbers, such that [MATH]f(-1) = 0[/MATH], [MATH]f(2) = 2[/MATH], and [MATH]\lim_{x\to \infty}\sin(f(x))[/MATH] exists.​

Is that correct?

Yes that is what I meant

 

[Dr.Peterson]

Except that I accidentally wrote f(2) = 2 where I meant f(1) = 2.

So, what are your thoughts on the problem? Please do as we ask, and not only quote the problem exactly as given, but also tell us what you have tried and where you are stuck.

Did lev888's question lead to any useful ideas? There are many possible answers, so I wouldn't even try to lead you toward one in particular -- we want you to use your own thinking to find an answer.

 

[Steven G]

Under which condition does [MATH]\lim_{x\to \infty}\sin(f(x))[/MATH] = sin([MATH]\lim_{x\to \infty}(f(x)[/MATH])? Or is it always true? If yes, then why?

I hope that after answering my questions then you can come up with a function?