Final answer:
The question involves examining properties of even functions, sine functions, and their products, with f(x) = x² being even and g(x) = sin(4x) representing an oscillatory sine function.
Step-by-step explanation:
The question asks about properties of functions, specifically even and odd functions, sine functions, and their multiplication. For an even function like f(x) = x², when it multiplies with another even function, the result is also even.
A sine function, g(x) = sin(4x), exhibits oscillatory behavior, going between +1 and -1 with a period related to the sine wave characteristics discussed in Figure 16.10, where it repeats every 2 radians. The product of an odd function times an even function does not have a general rule for symmetry, and the outcomes need to be evaluated on a case-by-case basis.