Show why, for linear functions, a vertical translation is equivalent to a horizontal translation. For a linear function, what horizontal translation is equivalent to a vertical translation of 3 units up? Alex says that the function f(x) = (3x)2 represents a vertical stretch of the quadratic parent function by a factor of 3. Marta says that it represents a horizontal compression by a factor of . Decide whether one student is correct, both are correct, or neither is correct.

For an unknown parent function f(x), write a function g(x) that is:
vertically stretched by a factor of 2,
shifted up 5 units, and
shifted right 4 units.
Explain how your function accomplishes these transformations.