Which graph represents the polynomial function h(x)=x^3+2x^2-11x-12

## Step 1: Find the roots of the polynomial<br />### To graph the polynomial, we first need to find its roots (x-intercepts). We can do this by factoring or using numerical methods. Since the polynomial is $h(x) = x^3 + 2x^2 - 11x - 12$, we can try integer factors of -12. We find that $h(3) = 27 + 18 - 33 - 12 = 0$, $h(-1) = -1 + 2 + 11 - 12 = 0$, and $h(-4) = -64 + 32 + 44 - 12 = 0$. Therefore, the roots are $x=3$, $x=-1$, and $x=-4$.<br /><br />## Step 2: Determine the end behavior<br />### As the leading term is $x^3$, the end behavior of the graph is as follows: as $x \to -\infty$, $h(x) \to -\infty$, and as $x \to \infty$, $h(x) \to \infty$.<br /><br />## Step 3: Sketch the graph<br />### Using the roots and the end behavior, we can sketch the graph. The graph passes through the x-axis at $x=-4$, $x=-1$, and $x=3$. It rises to the right and falls to the left.