Neural Networks as Function Finders

Imagine:

• All hard problems can essentially be boiled down to functions (well almost all of them). These could be:
  • $f(x)=y$
  • $f(\text{historical stocks data})=\text{Tomorrow’s stock price}$
  • $f(\text{image of a dog})=\text{the breed}$
  • $f(\text{the current position of a car, and all of it’s surroundings})=\text{the movement the wheels should take}$
• By training a Neural Networks, we’re simply undergoing a process to find the specific function. For the first one it could be easy. But for the others? How do we do it?