Question

describe the symmetry of this function. line symmetry only rotational symmetry only no symmetry both line and rotational symmetry

Explanation:

To determine the symmetry, we analyze the graph:

1. Line Symmetry: A graph has line symmetry if there's a line (axis) such that reflecting the graph over it maps the graph onto itself. For this function, there's no single line that reflects one part to the other (e.g., the y - axis doesn't work, nor does a horizontal or other vertical line).
2. Rotational Symmetry: A graph has rotational symmetry about the origin if rotating the graph 180° around the origin maps it onto itself. For this function, if we take a point \((x,y)\) on the graph, the point \((-x,-y)\) also lies on the graph (by observing the shape: the left - hand side and right - hand side are mirror images when rotated 180° around the origin). It does not have line symmetry (no axis of reflection), so it has rotational symmetry only.

Answer:

rotational symmetry only