Final answer:
The correct function for the student's distance from the finish line as he runs a 10-kilometer race with a pace of 1 kilometer every 4 minutes is d) f(x) = -1/4x + 10, considering the initial distance and the rate at which the distance decreases over time.
Step-by-step explanation:
The student is looking for a function that describes his distance from the finish line as he runs a 10-kilometer race at a pace of 1 kilometer every 4 minutes. To find the correct function, we must consider how distance to the finish changes over time.
At the start of the race, the student is 10 kilometers from the finish, so the function must have a y-intercept of 10. The student's speed is 1 kilometer every 4 minutes, which means the slope of the function will be negative (since he's getting closer to the finish), and the absolute value of this slope represents the speed.
Looking at the options provided, the correct answer is d) f(x) = -1/4x + 10. At the start (x=0), the student is 10 kilometers away, which matches the y-intercept of 10. For every 4 minutes that pass, he covers 1 kilometer, which is represented by the slope of -1/4.