Final answer:
The function that reflects the graph of f(x) = 2x across the y-axis and translates it up 5 units is f(x) = -2x + 5, which is option A.
Step-by-step explanation:
The student has asked which function transforms the graph of the parent function f(x) = 2x by reflecting it across the y-axis and translating it up 5 units. Reflecting a function across the y-axis means we should change the sign of x in the function. For the function f(x) = 2x, this reflection is achieved by making the function f(x) = -2x. Additionally, translating a function up by a certain number of units is done by adding that number to the whole function. Therefore, translating the reflected function up by 5 units gives us f(x) = -2x + 5.
A reflection across the y-axis changes the sign of the coefficient of x, hence the coefficient of x in the transformed function should be negative. The translation up by 5 units is indicated by the +5 at the end of the function. Thus, the correct transformation of the parent function f(x) = 2x that has been reflected across the y-axis and translated up 5 units is f(x) = -2x + 5. The appropriate answer to the question is option A).