An AI agent is being trained to navigate a grid world to reach a goal square. The original reward function, $r$, provides +10 for reaching the goal and -0.1 for every other step. To encourage faster learning, a new, transformed reward function, $r'$, is implemented. For a specific step that moves the agent from a square 5 units away from the goal to a square 4 units away, the agent receives a total transformed reward $r'$ of +0.9. Based on the general formula for reward shaping, $r'(s_t, a_t, s_{t+1}) = r(s_t, a_t, s_{t+1}) + f(s_t, a_t, s_{t+1})$, what are the numerical values for the original reward $r$ and the shaping function $f$ for this specific step? Explain the purpose of the shaping function in this context.