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 = x^3 for large values of |x|. (b) find the x - and y - intercepts of the graph of the function. the x - intercept(s) is/are . (simplify your answer. type an integer or a fraction. use a comma to separate answers as needed. type each answer only once.)

Explanation:

Step1: Find x - intercepts

Set $f(x)=0$, so $x^{2}(x + 3)=0$. By the zero - product property, if $ab = 0$, then $a=0$ or $b = 0$. Here, $x^{2}=0$ gives $x = 0$ and $x+3=0$ gives $x=-3$.

Step2: Find y - intercept

Set $x = 0$ in $f(x)$. Then $f(0)=0^{2}(0 + 3)=0$.

Answer:

The x - intercept(s) is/are $0,-3$