Question

Symmetry. Complete the graph using the given symmetry property.

Symmetry with respect to origin

Short answer

Symmetry with respect to the x-axis can be identified by replacing y by $-y$. The resulting equation is equivalent to the original one.

Symmetry with respect to the y-axis can be identified by replacing x by- x .The resulting equation is equivalent to the original one.

Symmetry with respect to the origin can be identified by replacing x by $-x$and y by $-y$. the resulting equation is equivalent to the original one

Step-by-step solution

Step 1. concept of symmetry.

Symmetry with respect to the x-axis can be identified by replacing y by $-y$. The resulting equation is equivalent to the original one.

Symmetry with respect to the y-axis can be identified by replacing x by- x .The resulting equation is equivalent to the original one.

Symmetry with respect to the origin can be identified by replacing x by $-x$and y by $-y$. the resulting equation is equivalent to the original one

Step 2. Given Graph.

Step 3. Completing the graph.

Since; the graph is symmetric about origin so the graph is rotated about the origin