Forecasting: How Decision Tree work?
Yes. It is also a function, but not an affine transformation of the input but a relatively complex sum of products of indicator functions of the input. Usually, this function is represented by the fitted tree and not as a formula.

So e.g. if you learn a tree of depth one and the split is at age 40 with mean response of 80 if age &lt; 40 and mean response of 100 if age $\ge$ 40, then the function could look like
$$
  \hat f(\text{age}, \text{income}) = 80 \cdot {\mathbf 1}\{\text{age} &lt; 40\} + 100 \cdot {\mathbf 1}\{\text{age} \ge 40\}
$$
You can maybe imagine how long the formula is if the depth is 7...