Question

determine if the graph is symmetric with respect to the x - axis, y - axis, or origin.

Explanation:

Step1: Check x - axis symmetry

If a graph is symmetric about the x - axis, for every point \((x,y)\) on the graph, the point \((x, - y)\) is also on the graph. Looking at the given graph, if we take a point above the x - axis, its reflection below the x - axis is not on the graph. So, it is not symmetric about the x - axis.

Step2: Check y - axis symmetry

If a graph is symmetric about the y - axis, for every point \((x,y)\) on the graph, the point \((-x,y)\) is also on the graph. Looking at the graph, if we take a point on the right - hand side of the y - axis, its reflection on the left - hand side of the y - axis is not on the graph. So, it is not symmetric about the y - axis.

Step3: Check origin symmetry

If a graph is symmetric about the origin, for every point \((x,y)\) on the graph, the point \((-x,-y)\) is also on the graph. Looking at the graph, if we take a point in the first quadrant, its reflection across the origin (in the third quadrant) is not on the graph. So, it is not symmetric about the origin.

Answer:

A. No symmetry