Chapter 1 - Graphs - 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry - 1.2 Assess Your Understanding - Page 17: 39

a) The point symmetric with respect to the x-axis is $(0,3)$ b) The point symmetric with respect to the y-axis is the point itself $(0,-3)$ c) The point symmetric with respect to the origin is also $(0,3)$

The point on the graph is $(0,-3)$ Symmetric with respect to the x-axis: if the point $(x,y)$ is on the graph then $(x,-y)$ is also on the graph. Symmetric with respect to the y-axis: if the point $(x,y)$ is on the graph then $(-x,y)$ is also on the graph. Symmetric with respect to the origin: if the point $(x,y)$ is on the graph then $(-x,-y)$ is also on the graph. Furthermore, the graph can be used as a proof of these statements. a) The point symmetric with respect to the x-axis is $(0,3)$ b) The point symmetric with respect to the y-axis is the point itself $(0,-3)$ c) The point symmetric with respect to the origin is also $(0,3)$