Question

ognize symmetry in functions
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:

• Line Symmetry: A graph has line symmetry if it can be folded over a line (the axis of symmetry) so that the two halves match. The given graph is symmetric about the \( y \)-axis (vertical line through \( x = 0 \)). If we fold the graph along the \( y \)-axis, the left and right halves coincide.
• Rotational Symmetry: A graph has rotational symmetry if it can be rotated about a point (usually the origin) by \( 180^\circ \) (or other angles) and map onto itself. For this graph, rotating \( 180^\circ \) about the origin would not map the graph onto itself (the "U - shaped" parts would not align). So, it only has line symmetry.

Answer:

line symmetry only