1. **Stating the problem:** Find the general antiderivative $F(x) + C$ of the function $f(x) = 2x - 4$. 2. **Formula used:** The antiderivative (indefinite integral) of a function $f(x)$ is given by $$F(x) = \int f(x) \, dx + C$$ where $C$ is the constant of integration. 3. **Apply the integral to each term:** $$F(x) = \int (2x - 4) \, dx = \int 2x \, dx - \int 4 \, dx$$ 4. **Integrate each term separately:** - For $\int 2x \, dx$, use the power rule $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$: $$\int 2x \, dx = 2 \int x^1 \, dx = 2 \cdot \frac{x^{1+1}}{1+1} = 2 \cdot \frac{x^2}{2} = x^2$$ - For $\int 4 \, dx$, since 4 is a constant: $$\int 4 \, dx = 4x$$ 5. **Combine the results:** $$F(x) = x^2 - 4x + C$$ 6. **Explanation:** The antiderivative reverses differentiation. Since the derivative of $x^2$ is $2x$ and the derivative of $-4x$ is $-4$, the antiderivative of $2x - 4$ is $x^2 - 4x$ plus an arbitrary constant $C$. **Final answer:** $$F(x) = x^2 - 4x + C$$