The function `y = f(x)` suffers the following transformations, indicated below, such that:

- translation 7 units down: subtract 7 from original function f(x)

`y = f(x) - 7`

- translation 4 units left: add a number inside original function f(x + 4)

`y = f(x + 4) - 7`

- a reflection in y axis

`y = f(x + 4) - 7`

- a stretch along y axis of factor 2 and translation up of 5 units

`y = 2f(x + 4) - 7 + 5 => y = 2f(x + 4) - 2`

- a translation right of 10 units, a reflection in x axis and a horizontal compression of factor 3

`y = 2f(x + 4 - 10) - 2` (a translation right of 10 units)

`y = -2f(x - 6) - 2` (a reflection in x axis)

`y = -2f(3(x - 6)) - 2` (a horizontal compression of factor 3)

**Hence, evaluating the final transformed function yields **`y = -2f(3(x - 6)) - 2.`