\text { Let us study the function } f(x)=\frac{x^{2}-4}{x^{2}-1} \text { . }

C) Find the first and second derivatives.

A) Find the domain of the function.

B) Find all asymptotes, intercepts, symmetries.

E) Study the function and its derivatives over its whole domain using the table of signs learned.

D) Find all critical points and potential inflection points.

F) Sketch the function to the best of your abilities, based on all details you found in this question so far.



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