Question

determine visually whether the graph is symmetric with respect to the x - axis, the y - axis, or the origin. is the graph symmetric with respect to the x - axis? yes no is the graph symmetric with respect to the y - axis? yes no is the graph symmetric with respect to the origin? yes no

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. Visually, if we reflect the graph across the x - axis, it does not match the original 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. Visually, if we reflect the graph across the y - axis, it does not match the original 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. Visually, if we rotate the graph 180 degrees about the origin, it does not match the original graph. So it is not symmetric about the origin.

Answer:

Is the graph symmetric with respect to the x - axis?
B. No
Is the graph symmetric with respect to the y - axis?
B. No
Is the graph symmetric with respect to the origin?
B. No