Final answer:
To find the reflection of the function f(x) = |x| over the x-axis, we simply negate the output of f(x), resulting in the function rule g(x) = -|x|.
Step-by-step explanation:
The student has asked to write a function rule for g(x) which is a reflection of f(x) over the x-axis. Given that the original function is f(x) = |x|, reflecting over the x-axis would invert the sign of the function's output. Therefore, the reflected function, g(x), will produce the negative value of f(x) for each x.
The new function rule for g(x) will be g(x) = -|x|. This is because reflection over the x-axis means that each output y in f(x) becomes -y in g(x). Therefore, if f(x) is positive (as |x| is always non-negative), g(x) will be the negative counterpart.