1. **State the problem:** We are given two functions $f(x) = -2x^2$ and $g(x) = -4x^2$ and the domain $-4 \leq x \leq -2$. We want to analyze these functions over this interval. 2. **Recall the formula:** Both functions are quadratic functions of the form $ax^2$ with negative coefficients, meaning they open downward. 3. **Evaluate the functions at the domain boundaries:** - For $x = -4$: $$f(-4) = -2(-4)^2 = -2 \times 16 = -32$$ $$g(-4) = -4(-4)^2 = -4 \times 16 = -64$$ - For $x = -2$: $$f(-2) = -2(-2)^2 = -2 \times 4 = -8$$ $$g(-2) = -4(-2)^2 = -4 \times 4 = -16$$ 4. **Interpretation:** Over the interval $-4 \leq x \leq -2$, $f(x)$ ranges from $-32$ to $-8$ and $g(x)$ ranges from $-64$ to $-16$. Since $g(x)$ has a larger negative coefficient, it decreases faster and is always less than or equal to $f(x)$ in this domain. 5. **Summary:** The functions are downward-opening parabolas with $g(x)$ steeper than $f(x)$ over the given domain. **Final answer:** $$f(-4) = -32, \quad f(-2) = -8$$ $$g(-4) = -64, \quad g(-2) = -16$$ $f(x)$ is always greater than or equal to $g(x)$ on $[-4, -2]$.