1: write a function that represents this process:

take a number, x.

multiply it by 4.

subtract 2 from the result.

then find the inverse of this function. does the inverse represent the reverse of the process above? explain why or why not.

2: 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?

3: 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 1/3. decide whether one student is correct, both are correct, or neither is correct.

4: 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.