Give an example of a continues function from an open and bounded interval $(a,b)\rightarrow I $ where $f(I)=ℝ$

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Give an example of a continues function from an open and bounded interval $(a,b)\rightarrow I $ where $f(I)=ℝ$

I'm having trouble coming up with a function that is has a bounded co-domain, yet an infinite domain for any values of a and b.

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Consider $\tan(x)$ restricted to the interval $(-\pi/2,\pi/2)$.