Question

which graph shows rotational symmetry?

Explanation:

Step1: Recall rotation - symmetry definition

A graph has rotational symmetry if it looks the same after a rotation of 180 - degrees about the origin. That is, if we replace \(x\) with \(-x\) and \(y\) with \(-y\), the equation of the graph remains the same.

Step2: Analyze each graph

For the first graph of \(f(x)\), if we rotate it 180 - degrees about the origin, the shape of the graph does not map onto itself.
For the second graph of \(g(x)\), if we rotate it 180 - degrees about the origin, the shape of the graph does not map onto itself.
For the third graph of \(k(x)\), if we rotate it 180 - degrees about the origin, the shape of the graph does not map onto itself.
For the fourth graph of \(h(x)\), which is a straight - line passing through the origin with a negative slope (\(y=-x\) type of line), when we rotate it 180 - degrees about the origin, the graph maps onto itself.

Answer:

The fourth graph (the graph of \(h(x)\)) shows rotational symmetry.