sketch the polynomial function using the following step - by - step process.\nf(x)=x^{2}(x - 6)\na…

Explanation:

Step1: Expand the polynomial

$$f(x)=x^{2}(x - 6)=x^{3}-6x^{2}$$ The leading term is (x^{3}) (degree (n = 3), which is odd, and leading coefficient (a=1>0)).

Step2: Determine end - behavior rules

For a polynomial (y = a_nx^{n}+a_{n - 1}x^{n-1}+\cdots+a_0) with (n) (degree) odd and (a_n>0): As (x\to-\infty), (y\to-\infty) (left - hand behavior). As (x\to+\infty), (y\to+\infty) (right - hand behavior).

Answer:

The left - hand behavior starts at (-\infty) and the right - hand behavior ends at (+\infty)