Question

samar sprints on a treadmill for 3 minutes. let f be the function that assigns his heart rate, in beats per minute, to each minute after he begins sprinting.
select the true statement.
a. the equation f(0) = 130 means that samars heart rate was 130 beats per minute after he finished sprinting.
b. the inequality f(3) > f(5) means that samars heart rate at 3 minutes is greater than his heart rate at 5 minutes.
c. the equation f(0) = f(5) means that samar sprinted for 5 minutes.
d. the inequality f(3) < f(5) means that samars heart rate at 3 minutes is greater than his heart rate at 5 minutes.

Explanation:

• Option A: \( f(0) \) represents the heart rate at 0 minutes (when he begins), not after finishing. So A is false.
• Option B: \( f(3) > f(5) \) means heart rate at 3 minutes is greater than at 5 minutes. This is a correct interpretation of the inequality for the function \( f \) (where \( f(t) \) is heart rate at time \( t \) minutes).
• Option C: \( f(0) = f(5) \) would mean heart rates at 0 and 5 minutes are equal, not that he sprinted for 5 minutes. So C is false.
• Option D: \( f(3) < f(5) \) would mean heart rate at 3 minutes is less than at 5 minutes, but the inequality here is misinterpreted in D (it says "greater" which is wrong for \( < \)). So D is false.

Answer:

B. The inequality \( f(3) > f(5) \) means that Samar's heart rate at 3 minutes is greater than his heart rate at 5 minutes.