Question

analyzing functional relationships
a game requires players to throw a ball into a target. the table shows values from the function that represents one path of a thrown ball, where x represents the horizontal distance the ball travels in feet and f(x) represents the height of the ball in feet.

x: 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5
f(x): 4, 13, 20, 25, 28, 29, 28

if the ball enters the target at the highest point in its path, based on the table, what is the height of the target?

options:
1.5 feet
28 feet
4 feet
29 feet

Explanation:

Step1: Identify the maximum height

We look at the values of \( f(x) \) (height) in the table: 4, 13, 20, 25, 28, 29, 28.

Step2: Determine the highest value

Among these values, 29 is the maximum. Now we find the corresponding \( x \)-value for \( f(x) = 29 \), which is \( x = 1.25 \). But the question is about the height of the target when the ball enters at the highest point. The highest height \( f(x) \) is 29 feet, and we check the options. The option with 29 feet is the height at the highest point.

Answer:

29 feet (the option corresponding to 29 feet, e.g., if the option is labeled as, say, C. 29 feet, then C. 29 feet)