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Is it possible to get a function from a domain of [1,infinity) and a range of (-2,infinity)? If so can someone provide an example of one or a graph? I did not think so because I thought that no matter what y value you had for x=1 then you could still get closer to -2, while not being -2.

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    $\begingroup$ By function you mean probably 'continuous or even cont.derivable? In either case, it surely exists. Just pinpoint an arbitrary (starting) value"$f(1)$ somewhere in the interval $(-2,\infty)$, and when you start drawing the function, just let it oscilate (so you go smoothly up and down), s.t.: -The first oscillation down comes to its (lowest) y-point at-1,9, the second one at-1,99; the third one at-1,999, etc.. - The oscillations up increase constatly (let's say by +1) with respect to the previous oscilation. I hope you get the idea. $\endgroup$ Sep 22 at 20:54
  • $\begingroup$ For example, $f(x) = \frac{2x}{x+1}\sin x + x(1 + \sin x)$. $\endgroup$ Sep 23 at 22:26

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