Final answer:
The student's question involves evaluating a piecewise defined function within specified intervals, graphing it properly, and understanding continuous probability distributions such as the uniform distribution where the probability density function is constant.
Step-by-step explanation:
The student's question pertains to a piecewise defined function and how to evaluate it within the given intervals. The function f(x) changes its rule depending on whether x is less than or equal to 4 or greater than 4. To graph this function, one would plot f(x) = x - 3 for x ≤ 4, resulting in a diagonal line that passes through the points (0, -3) and (4, 1). For x > 4, the graph follows f(x) = -2x + 8, which is a line with a negative slope that starts from the point (4, 1) and goes downwards.
Throughout the questions provided, the concept of a continuous probability distribution is explored, where probability is often interpreted as the area under the curve of the probability density function within a given interval. The uniform distribution is one where the probability density function f(x) is constant across the interval, leading to equal probabilities for equal-sized subintervals.