To answer this question, we need to analyze the function f(x) = 4·(1/2)^x carefully.
First, let's find the y-intercept which is the value of the function when x equals 0, that is, f(0). Substituting 0 in f(x) we get: f(0) = 4 * (1/2)^0 = 4 * 1 = 4. So, the y-intercept is 4.
Next, we'll analyze if the function is increasing or decreasing by examining the base of the exponential term, which is 1/2. If the base of the exponential part is greater than 1, the function would be increasing. Conversely, if the base is between 0 and 1, as is our case, the function is decreasing.
So, we can conclude that this function is decreasing.
In terms of the domain of the function, we inspect x and in our case, x can be any number because any real number can be an exponent. This means that the domain of f(x) is all real numbers.
Lastly, we consider the range of the function. Given that f(x) is always greater than 0, multiplied by 4 it will also be greater than 0. This means eventually the range of f(x) is all numbers greater than 0, which is usually denoted as (0, +∞).
So to summarize, the y-intercept is 4, the function is decreasing, the domain is all real numbers, and the range is (0, +∞). And, looking at our options, option a) matches all these characteristics. Thus, the correct answer is option a). Y-intercept: 4, Decreasing, Domain: All real numbers, Range: (0, +∞).