Question
A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y
, of the ball from he ground after x
seconds.
What is the range/ Interval notation.
HINT: How to write interval Notation for Quadratic Functions
(1 point)
Responses
2.5<x<5.5
2.5<x<5.5
0<x<5.5
0<x<5.5
0≤x≤2.5
0≤x≤2.5
x≥2
, of the ball from he ground after x
seconds.
What is the range/ Interval notation.
HINT: How to write interval Notation for Quadratic Functions
(1 point)
Responses
2.5<x<5.5
2.5<x<5.5
0<x<5.5
0<x<5.5
0≤x≤2.5
0≤x≤2.5
x≥2
Answers
GPT-4o mini
To determine the range of the height of the ball (y) as it is thrown from a cliff, we typically look at the height values in relation to the time (x).
Given that the ball is thrown from a height of 48 feet, the height (y) starts at 48 feet and eventually reaches 0 feet when the ball hits the ground. The graph should show that the height begins at 48, rises to a peak, and then falls back down to 0.
Given that the ball lands on the ground at some point after being thrown, the relevant heights (y) can be described as follows:
- The maximum height is 48 feet (at t=0).
- The minimum height when the ball is on the ground is 0 feet.
Thus, the range of heights (y) can be represented in interval notation as:
\[ 0 \leq y \leq 48 \]
However, to answer this question correctly, we need to find the correct interval provided in the options concerning time (x) rather than the direct height (y).
Based on the provided options:
1. \( 2.5 < x < 5.5 \)
2. \( 0 < x < 5.5 \)
3. \( 0 \leq x \leq 2.5 \)
4. \( x \geq 2 \)
The most logical interpretation is that the ball is in the air (with heights greater than 0) during some time interval. Assuming that “2.5” is the time when it touches the ground, one might conclude that there was time in the air before this point.
In this context, the best option that represents the time period in which the ball is above the height of zero would be:
**0 ≤ x ≤ 2.5**
This option correctly establishes that the ball is thrown from the cliff at 0 seconds and lands before or at 2.5 seconds.
Thus, if you are indeed looking for the time interval—then that would be the suitable choice.
Given that the ball is thrown from a height of 48 feet, the height (y) starts at 48 feet and eventually reaches 0 feet when the ball hits the ground. The graph should show that the height begins at 48, rises to a peak, and then falls back down to 0.
Given that the ball lands on the ground at some point after being thrown, the relevant heights (y) can be described as follows:
- The maximum height is 48 feet (at t=0).
- The minimum height when the ball is on the ground is 0 feet.
Thus, the range of heights (y) can be represented in interval notation as:
\[ 0 \leq y \leq 48 \]
However, to answer this question correctly, we need to find the correct interval provided in the options concerning time (x) rather than the direct height (y).
Based on the provided options:
1. \( 2.5 < x < 5.5 \)
2. \( 0 < x < 5.5 \)
3. \( 0 \leq x \leq 2.5 \)
4. \( x \geq 2 \)
The most logical interpretation is that the ball is in the air (with heights greater than 0) during some time interval. Assuming that “2.5” is the time when it touches the ground, one might conclude that there was time in the air before this point.
In this context, the best option that represents the time period in which the ball is above the height of zero would be:
**0 ≤ x ≤ 2.5**
This option correctly establishes that the ball is thrown from the cliff at 0 seconds and lands before or at 2.5 seconds.
Thus, if you are indeed looking for the time interval—then that would be the suitable choice.