1. **State the problem:** Determine the domain on which the function is increasing. 2. **Identify the function:** From the description, the function is a downward-opening parabola with vertex at approximately $(0,4)$ and x-intercepts near $-2$ and $2$. This suggests the function is of the form $$y = -a(x - 0)^2 + 4 = -a x^2 + 4$$ where $a > 0$. 3. **Recall the properties of a parabola:** For a parabola $y = -a x^2 + 4$, which opens downward, the vertex is the maximum point. The function increases on the interval to the left of the vertex and decreases to the right. 4. **Determine the increasing interval:** Since the vertex is at $x=0$, the function increases on the interval $$(-\infty, 0)$$ and decreases on $$(0, \infty)$$. 5. **Check the domain given by the x-intercepts:** The parabola crosses the x-axis at approximately $-2$ and $2$, so the function is defined at least on $[-2, 2]$. 6. **Combine the information:** The function is increasing on the interval from the left x-intercept to the vertex, i.e., $$[-2, 0]$$. **Final answer:** The function is increasing on the domain $$[-2, 0]$$.