Final answer:
The resulting function after translating the function f(x) = x^2 up 3 units, right 4 units, and reflecting it over the x-axis is g(x) = -((x - 4)^2 + 3).
Step-by-step explanation:
The student is asking about transformations of the function f(x) = x^2. Translating a function up 3 units involves adding 3 to the function, resulting in f(x) = x^2 + 3. Translating it to the right by 4 units shifts the function in the x direction, which is done by replacing the x with (x - 4), resulting in f(x) = (x - 4)^2 + 3.
Finally, reflecting a function over the x-axis changes the sign of the function's output. This changes f(x) to -f(x), giving us the transformed function g(x) = -((x - 4)^2 + 3), which is the final equation after performing all specified transformations.