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Consider the function \[ f(x)=\frac{x^{2}+1}{(x+2) \cdot(x+3)} \] Tick all of the following statements that are correct. \[ \lim _{x \rightarrow-\infty} f(x)=1 \text {. } \] \( y=f(x) \) has a horizontal asymptote at \( y=1 \). \[ \begin{array}{l} \lim _{x \rightarrow-2^{+}} f(x)=5 . \\ \lim _{x \rightarrow-3^{-}} f(x)=-\infty . \\ \lim _{x \rightarrow-3^{-}} f(x)=\infty . \end{array} \] \( y=f(x) \) has a horizontal asymptote at \( y=2 \). \[ \lim _{x \rightarrow \infty} f(x)=\infty \] \( y=f(x) \) has a vertical asymptote at \( x=-2 \).

We are given a function f(x)=x2+1(x+2).(x+3) We need to find which statements are correct

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