Chapter F - Foundations: A Prelude to Functions - Section F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry - F.2 Assess Your Understanding - Page 17: 37

a) The intercepts are at: $(-1,0)$ and $(1,0)$. b) The graph is symmetric with respect to the $x$-axis, $y$-axis and the origin.

a) The intercepts can be found at the intersection of the blue graph and the axes. Here, the graph only intersects the $x$-axis, the intercepts are at: $(-1,0)$ and $(1,0)$. b) If a graph is symmetric with respect to the $x$-axis then if the point $(x,y)$ is on the graph, then $(x,-y)$ is also on the graph. The graph is symmetric with respect to the $x$-axis since $(2, 2)$ and $(2, -2)$, as well as $(-2, 2)$ and $(-2, -2)$ (approximated values).are on the graph. If a graph is symmetric with respect to the $y$-axis then if the point $(x,y)$ is on the graph, then $(-x,y)$ is also on the graph. The graph is symmetric with respect to the $y$-axis since $(2, 2)$ and $(-2, 2)$, as well as $(2, -2)$ and $(-2, -2)$ (approximated values).are on the graph.. If a graph is symmetric with respect to the origin then if the point $(x,y)$ is on the graph, then $(-x,-y)$ is also on the graph; The graph is symmetric with respect to the origin since $(2, 2)$ and $(-2, -2)$, as well as $(-2, 2)$ and $(2, -2)$ (approximated values).are on the graph.