Going from y = x to y = 3x means we have vertically stretched everything by a factor of 3. For example, the point (4,4) moves to (4,12).
Then we replace x with (x-5) so that we get to y = 3(x-5). This shifts the graph 5 units to the right.
Finally, the -2 at the end shifts everything down 2 units.
---------------
Summary:
We applied these three transformations
- Vertically stretch by a factor of 3
- Shift 5 units to the right.
- Shift 2 units down
