Final answer:
The correct function describing the student's distance from the finish line after x minutes while running at a pace of 1 kilometer every 4 minutes is d) f(x) = -1/4x + 10.
Step-by-step explanation:
To find the function that describes the student's distance from the finish line after x minutes while running a 10-kilometer race at a pace of 1 kilometer every 4 minutes, we need a linear function with a negative slope, since the distance to the finish decreases as time increases. The rate at which the student runs is –1/4 km per minute (because 4 minutes is required to cover 1 km, thus in 1 minute, 1/4 km is covered). Taking into account that the total distance is 10 km, we can use the equation:
f(x) = -1/4x + 10
This equation means that starting at 10 km from the finish line (f(0) = 10), the student's distance from the finish line decreases by 0.25 km (or 1/4 km) for every minute that passes.
Therefore, the correct answer is d) f(x) = -1/4x + 10.