Question

consider the following graph: complete the sentences: the graph appears to be symmetric about the - axis symmetric about the - axis. symmetric about the origin. none of these. all of these

Explanation:

Step1: Recall symmetry definitions

A graph is symmetric about the y - axis if for every point (x,y) on the graph, the point (-x,y) is also on the graph. A graph is symmetric about the x - axis if for every point (x,y) on the graph, the point (x, - y) is also on the graph. A graph is symmetric about the origin if for every point (x,y) on the graph, the point (-x,-y) is also on the graph.

Step2: Examine the given graph

Looking at the graph, if we take a point on the right - hand side of the y - axis, there is no corresponding point on the left - hand side at the same y - value (so not symmetric about y - axis). If we take a point above the x - axis, there is no corresponding point below the x - axis at the same x - value (so not symmetric about x - axis). Since it is not symmetric about either the x - axis or y - axis, it cannot be symmetric about the origin.

Answer:

None of these