1. **State the problem:** Graph the function $g(x) = -3(x - 2)^2 + 4$ and identify its domain and range. 2. **Formula and rules:** This is a quadratic function in vertex form $g(x) = a(x-h)^2 + k$, where $(h,k)$ is the vertex. 3. **Identify vertex and shape:** Here, $a = -3$, $h = 2$, and $k = 4$. Since $a < 0$, the parabola opens downward. 4. **Domain:** The domain of any quadratic function is all real numbers, so $\text{Domain} = (-\infty, \infty)$. 5. **Range:** Because the parabola opens downward and vertex is the maximum point, the range is $g(x) \leq 4$, or $(-\infty, 4]$. 6. **Graph features:** Vertex at $(2,4)$, parabola opens downward, vertically stretched by factor 3. **Final answer:** - Domain: $(-\infty, \infty)$ - Range: $(-\infty, 4]$