Question

a fountain sprays water into a pool as part of the filtration system. the projected path of water is modeled by the function given in the table, where x represents the time in seconds since the water left the fountain and f(x) represents the height in feet above the pool’s water line.

x	f(x)
1	2
2	1.5
3	0
4	-2.5
5	-6

how many seconds does the water travel through the air?

• -6
• 1.5
• 3
• 5

Explanation:

Step1: Understand the problem

We need to find the time the water travels through the air. The height \( f(x) \) is above the pool's water line when the water is in the air. When \( f(x) = 0 \), the water hits the pool (stops being in the air). We look for the \( x \) value when \( f(x)=0 \).

Step2: Analyze the table

From the table, when \( x = 3 \), \( f(x)=0 \). Before \( x = 3 \), the height is positive (above water), and after \( x = 3 \), it's negative (below water). So the water is in the air from \( x = 0 \) to \( x = 3 \), so the time in air is 3 seconds.

Answer:

3 (corresponding to the option "3")