The function \( j(x) = 15x - 12 \) can be analyzed by breaking it down into the transformations applied to its parent function, which is \( f(x) = x \).
- The term \( 15x \) indicates a vertical stretch by a factor of 15.
- The term \(-12\) indicates a vertical shift downward, specifically 12 units.
Thus, the correct transformation of the function is a vertical shift down 12 units.
The correct response is: vertical shift down 12 units.