5.2E: Funções de potência e funções polinomiais (exercícios)

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Para os exercícios a seguir, determine se a função é uma função polinomial e, em caso afirmativo, forneça o grau e o coeficiente inicial.

7. $$f(x)=4 x^{5}-3 x^{3}+2 x-1$$

8. $$f(x)=5^{x+1}-x^{2}$$

9. $$f(x)=x^{2}\left(3-6 x+x^{2}\right)$$

Para os exercícios a seguir, determine o comportamento final da função polinomial.

10. $$f(x)=2 x^{4}+3 x^{3}-5 x^{2}+7$$

11. $$f(x)=4 x^{3}-6 x^{2}+2$$

12. $$f(x)=2 x^{2}\left(1+3 x-x^{2}\right)$$