Final answer:
The correct parent function whose value doubles with each increase of 1 in the value of x is y = 2^x, which is an exponential function. Other provided options do not exhibit such exponential growth.
Step-by-step explanation:
The student's question concerns a function whose value doubles for each increase of 1 in the value of x. Given the options, the parent function that matches this description is y = 2x. This is because an exponential function like 2x increases by a factor of the base (which is 2 in this case) for each unit increase in x. The graph of this function will show that as x increases by 1, the value of y doubles.
None of the other functions listed (y = x2, y = |x|, y = √x) have the characteristic that their output doubles for each single increment in x. A quadratic function y = x2 increases quadratically, not exponentially. The absolute value function y = |x| increases linearly, and the square root function y = √x increases in a sub-linear fashion (slower than linear).