Question

which functions are symmetric about the y - axis? check all of the boxes that apply.

Explanation:

Step1: Define y-axis symmetry

A function is symmetric about the y-axis if for every point $(x, y)$ on the graph, the point $(-x, y)$ also lies on the graph (even function property).

Step2: Analyze first graph

The graph mirrors perfectly across the y-axis: for every $(x,y)$, $(-x,y)$ exists.

Step3: Analyze second graph

The graph does not mirror across the y-axis: points like $(2,1)$ exist but $(-2,1)$ does not (instead $(-2,-1)$ is present, showing origin symmetry).

Step4: Analyze third graph

The graph mirrors perfectly across the y-axis: for every $(x,y)$, $(-x,y)$ exists.

Answer:

Check the boxes for the first graph (top) and third graph (bottom).