1. **State the problem:** We are given the function $f(x) = -x^3 + \frac{2}{3}$ and asked to find $f(x) + 2$ expressed as a polynomial in standard form. 2. **Recall the formula:** Adding a constant to a function shifts its graph vertically. Algebraically, $f(x) + 2 = \left(-x^3 + \frac{2}{3}\right) + 2$. 3. **Perform the addition:** $$f(x) + 2 = -x^3 + \frac{2}{3} + 2$$ 4. **Convert 2 to a fraction with denominator 3:** $$2 = \frac{6}{3}$$ 5. **Add the fractions:** $$\frac{2}{3} + \frac{6}{3} = \frac{8}{3}$$ 6. **Write the final polynomial in standard form:** $$f(x) + 2 = -x^3 + \frac{8}{3}$$ **Answer:** The polynomial $f(x) + 2$ in standard form is $$-x^3 + \frac{8}{3}$$.