Question

graph the polynomial function f(x)=x^2(x + 3) using parts (a) through (e). (a) determine the end behavior of the graph of the function. the graph of f behaves like y = for large values of |x|.

Explanation:

Step1: Expand the polynomial

$f(x)=x^{2}(x + 3)=x^{3}+3x^{2}$

Step2: Analyze end - behavior

For large values of $|x|$, the leading - term of the polynomial dominates the behavior of the function. The leading term of $f(x)=x^{3}+3x^{2}$ is $x^{3}$.

Answer:

$x^{3}$