Which two transformations must be applied to the graph of y = ln(x) to result in the graph of y = –ln(x) + 64?

The negative sign in −ln(x) reflects the graph of y = ln(x) across the x-axis. Adding 64 shifts the reflected graph vertically upward by 64 units. Therefore, the transformations are a reflection over the x-axis and a vertical translation.

AI-written and checked against the verified answer.