



 
Hi Rimoshika, I would define the function in two pieces, one for $x < 1$ and the other for $x > 1.$ I can help with the part for $x < 1.$ For $x < 1$ define a function $f(x) = g(x) \sin x$ where $g(x)$ is a function that satisfies $\lim g(x) = 1$ as $x \rightarrow \infty$ and $\lim g(x) = \pm \infty$ as $x \rightarrow 1.$ The $f(x)$ will have $y = \sin x$ and $x =1$ as asymptotes. Harley  


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