Question

The function f(z) = 26.2 - 0.1z models the distance a runner is from the finish line of a race 26.2 miles long, where › represents the number of minutes running from the 50-minute mark through the 100-minute mark of the race. what is the practical range of the function?

a. All integers
b.All real numbers between 16.2 and 21.2 inclusive
c. Integers from 50 to 100 inclusive
d.All real numbers between 50 and 100 inclusive

Answer 1

The practical range of the function f(z) = 26.2 - 0.1z, which represents the distance a runner is from the finish line of a marathon after the 50-minute mark, is all real numbers between 16.2 and 21.2 inclusive. This accounts for the distances from the finish line when the time is between 50 and 100 minutes.

Step-by-step explanation:

The function given is f(z) = 26.2 - 0.1z, which models the distance a runner is from the finish line in a 26.2-mile race, with respect to time in minutes after the 50-minute mark.

To find the practical range of the function, we consider the context of the problem, which is the runner's distance from the finish line between the 50-minute and 100-minute marks. As the runner moves forward, the distance decreases. When z = 50, f(z) = 26.2 - 0.1(50) = 21.2. When z = 100, f(z) = 26.2 - 0.1(100) = 16.2. Therefore, the practical range includes all distances the runner can be from the finish line between the times of 50 and 100 minutes, which are all real numbers from 16.2 to 21.2 inclusive. Hence, the correct answer is All real numbers between 16.2 and 21.2 inclusive.