Question
A football is thrown into the air. It reaches a maximum height of 18 yards and lands 78 yards from where it was thrown. Which answer option represents the domain, in terms of the context?(1 point)
Responses
x=
all real numbers
x equals all real numbers
18≤x≤78
18 less-than-or-equal-to x less-than-or-equal-to 78
0≤x≤78
0 less-than-or-equal-to x less-than-or-equal-to 78
0≤x≤18
Responses
x=
all real numbers
x equals all real numbers
18≤x≤78
18 less-than-or-equal-to x less-than-or-equal-to 78
0≤x≤78
0 less-than-or-equal-to x less-than-or-equal-to 78
0≤x≤18
Answers
GPT-4o mini
To determine the correct domain in the context of the football's trajectory, we need to consider the relevant values of \( x \), which represents the horizontal distance from the point where the football was thrown.
- The football reaches its maximum height at some point in its trajectory, but the height does not impact how far it travels horizontally.
- It lands 78 yards from the starting point, so the horizontal distance \( x \) must start from 0 (the point where it was thrown) and go up to 78 (where it lands).
Given this context, the appropriate domain would be:
**0 ≤ x ≤ 78**
This indicates that the football travels horizontally from 0 yards at the throw to 78 yards at the landing point. Therefore, this option correctly represents the domain.
- The football reaches its maximum height at some point in its trajectory, but the height does not impact how far it travels horizontally.
- It lands 78 yards from the starting point, so the horizontal distance \( x \) must start from 0 (the point where it was thrown) and go up to 78 (where it lands).
Given this context, the appropriate domain would be:
**0 ≤ x ≤ 78**
This indicates that the football travels horizontally from 0 yards at the throw to 78 yards at the landing point. Therefore, this option correctly represents the domain.