Question

An elevator in a tall building starts at a height of 9 m and descends at a rate of 4 m/s for a total of six seconds. Write a function to model the situation, where X is the time and FX is the height of the elevator. What is the domain and range for this situation?

A. Domain: [0, 6]; Range: [9, -15]
B. Domain: All Real Numbers; Range: [9, -15]
C. Domain: [0, 6]; Range: All Real Numbers
D. Domain: All Real Numbers; Range: All Real Numbers

Answer 1

The height of the descending elevator can be described by the function F(x) = 9 - 4x. The domain is [0, 6] seconds and the range is [9, -15] meters, making option A the correct choice.

Step-by-step explanation:

To model the elevator's height over time, we need a linear function that accounts for its initial height and the rate of descent.

Since the elevator starts at 9 m and descends at a rate of 4 m/s, the function should reflect a decrease of 4 meters for every second that passes. The function F(x) = 9 - 4x represents the height of the elevator, with x being the time in seconds.

The domain of this function reflects the time interval during which the descent is occurring, which is from x = 0 to x = 6 seconds, hence the domain is [0, 6]. Regarding the range, since the elevator begins at 9 m and descends for 6 seconds, the final height will be 9 m - 4 m/s * 6 s = -15 m (recognizing that the negative signifies a descent below the starting point, which could be below ground level in this context). Consequently, the range is [9, -15].

Hence, the correct option is A.