To solve this problem, we need to determine the function $f(x)$ based on the graph provided and additional information. Here’s the step-by-step approach:

Step 1: Identify the Roots

From the graph, it appears that the polynomial has roots at approximately $x = -4$, $x = 0$, and $x = 4$. This suggests that $f(x)$ could be expressed in factored form as: $f(x) = a(x + 4)(x)(x - 4)$ which simplifies to: $f(x) = a(x + 4)x(x - 4) = a(x^3 - 16x)$

Step 2: Use the Given Point to Find $a$

We know that the point $(0, 90)$ is on the graph. Substitute $x = 0$ and $f(0) = 90$ into the equation to solve for $a$.

Substitute $x = 0$ in the equation $f(x) = a(x^3 - 16x)$: $f(0) = a(0^3 - 16 \cdot 0) = a \cdot 0 = 0$

However, based on the context, it seems there may be an error in the setup because