Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises - Page 11: 78

The equation is symmetric about the $x$-axis, the $y$-axis and the origin.

$|x|+|y|=1$ Check for symmetry about the $y$-axis by substituting $x$ by $-x$ in the given function and simplifying: $|-x|+|y|=1$ $|x|+|y|=1$ Since substituting $x$ by $-x$ yielded an equivalent expression, the equation is symmetric about the $y$-axis. Check for symmetry about the $x$-axis by substituting $y$ by $-y$ in the given function and simplifying: $|x|+|-y|=1$ $|x|+|y|=1$ Since substituting $y$ by $-y$ yielded an equivalent expression, the equation is symmetric about the $x$-axis. Since the equation is symmetric about both the $x$ and $y$-axis, it is also symmetric about the origin. The graph is shown in the answer section.