The function f(x) is the number of feet below the surface of the water a diver is at x seconds. After 14 s, the diver reached the maximum distance of 22 ft below the surface of the water. The diver stayed in the water for 20 minutes.
What is the practical domain for the function f(x)?
[0,1200]
all negative real numbers
all positive real numbers
[−22,0]
x is the time, not the depth. They used x instead of t to confuse you. Negative times are unusual.
To determine the practical domain for the function f(x), we need to consider the given information. The function represents the number of feet below the surface of the water a diver is at x seconds. We are also told that the diver stayed in the water for 20 minutes, which is equivalent to 20 × 60 = 1200 seconds.
Since the function describes the distance below the surface of the water, it cannot be negative as the diver cannot be above the surface. Thus, the practical domain of the function f(x) must include only non-negative numbers.
Furthermore, we know that the diver reached the maximum distance of 22 ft below the surface after 14 seconds. This means that the function is defined for at least 14 seconds and extends beyond that. Therefore, the practical domain of the function f(x) is [0, 1200].
Hence, the answer is [0, 1200].