Question

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

Explanation:

Step1: Recall y - axis symmetry definition

A function is symmetric about the y - axis if for every point \((x,y)\) on the graph, the point \((-x,y)\) is also on the graph. Visually, the left - hand side of the y - axis is a mirror image of the right - hand side.

Step2: Analyze first graph

The first graph has a wave - like shape. If we take a point \((x,y)\) on the right - hand side of the y - axis, we can find a corresponding point \((-x,y)\) on the left - hand side with the same y - value. So, it is symmetric about the y - axis.

Step3: Analyze second graph

The second graph does not have y - axis symmetry. For example, if we consider a point on the right - hand side curve away from the origin, there is no corresponding point on the left - hand side with the same y - value.

Step4: Analyze third graph

The third graph is a parabola opening upwards with its vertex on the y - axis. For any point \((x,y)\) on the right - hand side of the y - axis, we can find a point \((-x,y)\) on the left - hand side with the same y - value. So, it is symmetric about the y - axis.

Answer:

The first and third functions are symmetric about the y - axis.