Sum of two absolute values

Consider the graph of $y = |x + 1| + |x - 1|$, the sum of the distances from a point $x$ on the number line to $-1$ and to $1$.

For $-1 \le x \le 1$ it is constant, $(x + 1) + (1 - x) = 2$, so the graph is flat. For $x > 1$ it is $2x$, and for $x < -1$ it is $-2x$, rising with slope $\pm 2$. The corners are at $(-1, 2)$ and $(1, 2)$, and the flat bottom is the minimum value $2$. The large dots mark the corners and the middle point $(0, 2)$.