The problem asks to graph the function $f(x) = x^3 - 4$.

1. Problem Description

The problem asks to graph the function $f(x) = x^3 - 4$.

2. Solution Steps

To graph the function $f(x) = x^3 - 4$, we can analyze it as a transformation of the basic cubic function $y = x^3$. The given function is a vertical translation of the basic cubic function by $-4$ units. This means we shift the graph of $y = x^3$ downward by 4 units.

First, let's find some key points on the graph of $y = x^3$:

- When $x = 0$, $y = 0^3 = 0$.

- When $x = 1$, $y = 1^3 = 1$.

- When $x = -1$, $y = (-1)^3 = -1$.

- When $x = 2$, $y = 2^3 = 8$.

- When $x = -2$, $y = (-2)^3 = -8$.

Now, apply the vertical translation by subtracting 4 from each $y$-coordinate:

- When $x = 0$, $f(0) = 0^3 - 4 = -4$.

- When $x = 1$, $f(1) = 1^3 - 4 = 1 - 4 = -3$.

- When $x = -1$, $f(-1) = (-1)^3 - 4 = -1 - 4 = -5$.

- When $x = 2$, $f(2) = 2^3 - 4 = 8 - 4 = 4$.

- When $x = -2$, $f(-2) = (-2)^3 - 4 = -8 - 4 = -12$.

Thus, the key points on the graph of $f(x) = x^3 - 4$ are: $(0, -4)$, $(1, -3)$, $(-1, -5)$, $(2, 4)$, and $(-2, -12)$.

The graph will look like a cubic function that has been shifted down by 4 units.

3. Final Answer

$f(x) = x^3 - 4$