Question

for each graph, select all symmetries that apply. for each graph, select all symmetries that apply. graph 1 symmetry: x - axis y - axis origin none of these graph 2 symmetry: x - axis y - axis origin none of these graph 3 symmetry: x - axis y - axis origin none of these

Explanation:

Step1: Analyze Graph 1

A line \(y = -x\) is symmetric about the origin. If \((x,y)\) is on the line, then \((-x,-y)\) is also on the line. It is not symmetric about the \(x -\)axis or \(y -\)axis.

Step2: Analyze Graph 2

The semi - circle is not symmetric about the \(x -\)axis (as it is only a semi - circle), not symmetric about the \(y -\)axis (since it is not centered symmetrically about the \(y -\)axis in the standard sense here), and not symmetric about the origin.

Step3: Analyze Graph 3

The diamond - shaped figure is symmetric about the \(x -\)axis (if \((x,y)\) is on the figure, then \((x, - y)\) is on the figure), symmetric about the \(y -\)axis (if \((x,y)\) is on the figure, then \((-x,y)\) is on the figure), and symmetric about the origin (if \((x,y)\) is on the figure, then \((-x,-y)\) is on the figure).

Answer:

Graph 1: origin
Graph 2: none of these
Graph 3: x - axis, y - axis, origin