Final answer:
The correct function notation for the geometric sequence 4, 2, 1, 1/2, 1/4,... is D) f(x) = 4 * (1/2)^(x-1), with 4 as the first term and 1/2 as the common ratio.
Step-by-step explanation:
To write the given geometric sequence in function notation, we need to identify the first term (a) and the common ratio (r) of the sequence.
The geometric sequence given is 4, 2, 1, 1/2, 1/4,... This sequence starts with a = 4 and the common ratio r can be found by dividing the second term by the first term, which gives us 2/4 = 1/2. We can express the nth term of a geometric sequence with the formula a_n = a * r^(n-1), where a is the first term, r is the common ratio, and n is the term number.
If we want to use function notation, such as f(x), the formula becomes f(x) = a * r^(x-1). In this case, the function that represents the geometric sequence is f(x) = 4 * (1/2)^(x-1).
Therefore, the correct option is D) f(x) = 4 * (1/2)^(x-1).