What Is a Function Transformation?

You have the graph of $y = |x|$ and decide to make another graph, for a function $z,$ where you randomly do a horizontal translation of $y$ of size $-1, 0,$ or $1,$ and then randomly do a vertical translation of size $-1, 0,$ or $1.$ What is the probability that the graphs of $y$ and $z$ intersect at least once?