Question

graph the polynomial function f(x)=x^3 + x^2 - 6x. answer 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 . (type an integer or a simplified fraction. use a comma to separate answers as needed. type each answer only once.)

Explanation:

Step1: Find x - intercepts

Set $f(x)=0$, so $x^{3}+x^{2}-6x = 0$. Factor out an $x$ first: $x(x^{2}+x - 6)=0$. Then factor the quadratic: $x(x + 3)(x - 2)=0$. Using the zero - product property, $x=0$ or $x+3=0$ or $x - 2=0$. So $x=0,x=-3,x = 2$.

Step2: Find y - intercept

Set $x = 0$ in $f(x)$. Then $f(0)=0^{3}+0^{2}-6\times0=0$.

Answer:

The x - intercept(s) is/are $0,-3,2$; The y - intercept is $0$