1. **State the problem:** Find the value of $x$ such that $f(x) = \sqrt[3]{x - 2} = 0$. 2. **Recall the formula and rule:** The cube root function $\sqrt[3]{y}$ equals zero if and only if $y = 0$. 3. **Set the inside of the cube root equal to zero:** $$\sqrt[3]{x - 2} = 0 \implies x - 2 = 0$$ 4. **Solve for $x$:** $$x - 2 = 0$$ $$\cancel{x} - 2 + 2 = \cancel{0} + 2$$ $$x = 2$$ 5. **Interpretation:** The function $f(x)$ equals zero at $x = 2$. This is the $x$-intercept of the graph. **Final answer:** $$x = 2$$