Final answer:
The correct function to describe the student's distance from the finish line after x minutes is f(x) = -4x + 10. This linear function takes into account the fact that the student runs at a rate of 1 kilometer every 4 minutes and starts 10 kilometers from the finish line.
Step-by-step explanation:
The student is looking for a function that describes their distance from the finish line after x minutes in a 10-kilometer race where they run 1 kilometer every 4 minutes. To find the correct function, it's important to understand that the distance from the finish line decreases as time passes.
Initially, the student is 10 kilometers away from the finish line. Since the student runs at a rate of 1 kilometer every 4 minutes, we can say that for every 4 minutes that pass (x/4), the student covers 1 kilometer. So we want to find a function f(x) that gives the remaining distance to the finish line. The correct function would be f(x) = -4x + 10.
This is because for every 4 minutes, the student is 1 kilometer closer to the finish line, which corresponds to a slope of -1/4 when considering the rate as kilometers per minute. However, we know that x is in minutes, so we need to multiply by 4 to get the correct number of kilometers. Therefore, the rate of distance change is -4 km per minute, and because the student starts 10 kilometers away, the y-intercept is 10.