1. Given the sets $A=\{(x, y) \mid y=a x+2\}, B=$ $\{(x, y) \mid y=| x+1 |\}$, and $A \cap B$ is a singleton set, then the range of the real number $a$ is $\qquad$ .
1. Solution: Draw the graph of the function $y=|x+1|$, then discuss the position of the line $y=a x+2$. From the graph, we can see: when $a \geqslant 1$, $A$ $\cap B$ is a singleton set; when $-1<a<1$, $A \cap B$ is a two-element set; when $a \leqslant$ -1, $A \cap B$ is also a singleton set. Therefore, the range of values for $a$ is $(-\infty, 1] \cup[1,+\infty]$