Question

Symmetry. Complete the graph using the given symmetry property.

Symmetry with respect to the y-axis.

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 with respect to the y-axis so graph in the 3^rd quadrant should be similar to the graph in the first quadrant.