This graph has rotational symmetry about the point
The Correct Answer and Explanation is:
✅ Correct Answer: (0, 0)
📘 Explanation
The graph in the image shows a smooth S-shaped curve passing through the origin (0,0)(0, 0), increasing from the bottom left to the top right. This is the characteristic shape of odd functions such as y=x3y = x^3 or similar cubic functions.
🔄 What Is Rotational Symmetry?
A graph has rotational symmetry about a point if rotating the graph 180 degrees around that point results in the same graph. In simpler terms, the graph looks identical upside down if you spin it halfway around that central point.
📌 Identifying the Center of Rotation
To find the center of rotational symmetry:
- Look for a point where the graph is “balanced.”
- In this case, the curve passes through the origin and mirrors itself diagonally.
- If you rotate the graph 180° about the origin (0, 0), the top right part maps onto the bottom left, and vice versa.
This shows the graph is symmetric around the origin.
🧠 Mathematical Reasoning
The graph represents an odd function. A function is odd if: f(−x)=−f(x)f(-x) = -f(x)
This property means that if you take a point (x,y)(x, y) on the graph, the point (−x,−y)(-x, -y) is also on the graph — which is exactly what happens with 180° rotational symmetry about the origin.
🔍 Conclusion
The correct point of rotational symmetry is:
(0,0)\boxed{(0, 0)}
This symmetry is a defining feature of many cubic and other odd-degree functions, and recognizing it helps understand their graphical behavior.
