r/HomeworkHelp • u/Kobrazak University/College Student • 19h ago

Further Mathematics [College - Polynomial Functions)

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For d) the book states: Determine the end behavior (which I’ve done), and find the power function that the graph of f resembles for large values of |x|. How do you get y=7x7? Is it because 7 is the leading term, has no variable, and it’s a 7th degree polynomial? TIA

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u/GammaRayBurst25 19h ago

Factor out 7 factors of x to get 7(x^2+4)^2(x-5)^3=7x^7(1+4/x^2)^2(1-5/x)^3.

In the limit where |x| is very large, 4/x^2 and 5/x become negligible. As such, asymptotically, the function tends to 7x^7.

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u/Kobrazak University/College Student 18h ago

How did you factor 7x7 (1+4/x2)2(1-5/x)3? How did you figure that out?