Final answer:
The student seems to be asking about two different functions: the rational function f(x) = (x-7)/(4x^2-4x+1) and the constant function f(x) = 20 or f(x) = 8, which are described by horizontal lines within their given intervals. For the constant functions, the graph would be a horizontal line at the specified y-value, and in the case of f(x) = 8, any x-value between 2.5 and 7.5 satisfies P(2.5 < x < 7.5).
Step-by-step explanation:
The student is asking about the behavior of the function f(x) = (x-7)/(4x^2-4x+1) for a real number x. To better understand this function's behavior, one would typically analyze its graph, look for asymptotes, intercepts, and intervals of increase or decrease. However, it seems there might be some confusion in the question, as there's a reference to a horizontal line graph of f(x) = 20, which is different from the function provided.
For the function f(x) = 20 for 0 ≤ x ≤ 20, the graph would indeed be a horizontal line at the y-level of 20 within the restricted domain. Moreover, if considering the function f(x) = 8 for the interval 0 ≤ x ≤ 8, its graph would be a horizontal line at y = 8, and the probability P(2.5 < x < 7.5) would imply any value of x between 2.5 and 7.5 since all y-values are equal to 8 within this domain, making the probability equal to 1 within this given interval.