Question

1. which of the following is the graph of the function $f(x)=x(x + 3)(x - 3)$?

Explanation:

Step1: Find x-intercepts

Set $f(x)=0$, solve $x(x+3)(x-3)=0$.
Solutions: $x=-3, x=0, x=3$.

Step2: Determine end behavior

Expand $f(x)$: $f(x)=x(x^2-9)=x^3-9x$.
Leading term is $x^3$, so as $x\to+\infty$, $f(x)\to+\infty$; as $x\to-\infty$, $f(x)\to-\infty$.

Step3: Match to graph

Only the bottom-right graph has x-intercepts at -3, 0, 3 and follows the end behavior of a positive cubic function (falls left, rises right, with two turning points).

Answer:

The bottom-right graph (the one with x-intercepts at -3, 0, 3, starting downward from the left, peaking, then dipping, then rising upward to the right)