Show that for every $x \in \mathbb{N}$ the function $A_x(y) = A(x,y)$ is primitive recursive, with $A(x,y): \mathbb{N} \times \mathbb{N} \to \mathbb{N}$ being the Ackermann function
I need some initial advice how to attack this problem. Since the Ackermann function is known to be not primitive recursive, I think the problem wants me the show that it is primitive recursive for every $n$, with $y$ staying unchanged? My initial thought was to define $A(x+1,y)$ and $A(x,0$) and show that each are primitive recursive.