Question

¿qué gráfico muestra simetría rotacional?

Explanation:

To determine which graph shows rotational symmetry, we analyze each:

1. First graph (parabola): Symmetry about the \( y \)-axis (reflectional), not rotational (needs \( 180^\circ \) rotation to map onto itself, but a parabola does not).
2. Second graph (wavy curve): No rotational symmetry (rotation would not align it with itself).
3. Third graph (V - shape): Symmetry about the \( y \)-axis (reflectional), not rotational.
4. **Fourth graph (exponential - like? Wait, no—wait, let's check \( 180^\circ \) rotation. If we rotate the fourth graph \( 180^\circ \) around the origin, does it map to itself? Wait, maybe I mislabeled. Wait, actually, the key is: A graph has rotational symmetry if rotating it \( 180^\circ \) around a point (usually the origin) maps it to itself. Let's re - evaluate. Wait, maybe the fourth graph: Let's take a point, say \( (1,1) \), rotating \( 180^\circ \) gives \( (- 1,-1) \). Does the graph pass through \( (-1,-1) \)? If the left - hand part goes through \( (-1,-1) \), then yes. Wait, maybe the fourth graph is the one with rotational symmetry. Wait, maybe I made a mistake earlier. Wait, the first three have reflectional symmetry (about \( y \)-axis), but rotational symmetry (order 2, \( 180^\circ \)) means that rotating \( 180^\circ \) around the origin (or a center) maps the graph to itself. Let's check the fourth graph: If we rotate it \( 180^\circ \), the direction of the curve and the points should match. So the graph with rotational symmetry is the fourth one (assuming the left - hand part and right - hand part are related by \( 180^\circ \) rotation).

Answer:

The fourth graph (the one on the far right) shows rotational symmetry.