Assume that the graph has Origin symmetry. Select the complete graph of the equa- tion.

Question

Quizplus · Accepted Answer

If a graph has origin symmetry, it means that if a point (x,y) is on the graph, then the point (-x,-y) is also on the graph. This can only occur if the equation is symmetric with respect to the origin, which means that if you replace x with -x and y with -y, the equation remains unchanged.

In option A, the equation is y = |x|. If we replace x with -x and y with -y, we get -y = |-x|. But |-x| is the same as |x| since the absolute value of a number is always positive. So we can rewrite the equation as -y = |x|, which is the same as the original equation y = |x| since the negative sign can be moved over to either side. Therefore, option A is the correct choice.

Options B, C, D, and E do not have origin symmetry because if we replace x with -x and y with -y, the equation does not remain unchanged.

Assume That the Graph Has Origin Symmetry