Final answer:
To estimate f(2), interpolation or trend analysis is used. To find when f(x) is positive, intervals where f(x) > 0 in the table are identified. For P(0 < x < 12), with f(x) given as 12 over [0, 12], the probability is 1.
Step-by-step explanation:
The student is asking how to estimate the value of f(2) using a given table of values for a function f(x) and for what values of x does f(x) appear to be positive. Without the table provided, a general approach can be given. To estimate f(2), one could use the values of f(x) that are closest to x=2 on the table and then, depending on whether the function is linear or not, use interpolation or a best guess based on the trend of the values. To determine where f(x) is positive, one would review the table and note all intervals in the domain of f(x) where the function's value is above zero.
To answer the specific probability function question regarding P(0 < x < 12), since f(x) is given as a continuous probability function that equals 12 over the interval [0, 12], then the total probability over this interval is 1. Therefore, the probability P(0 < x < 12) is simply 1.