Question
The graph shows the total amount of chips in the bag in oz., y, over time, x, in minutes. It's a negative slope with the equation: x + 2y = 7 and 2 points: point 1: (0, 3.5) and point 2: (7, 0)
What is the end behavior of the graph? Response area
2) What would be a reasonable domain for this scenario? Response area
3) What would be reasonable outputs for the scenario domain?
What is the end behavior of the graph? Response area
2) What would be a reasonable domain for this scenario? Response area
3) What would be reasonable outputs for the scenario domain?
Answers
GPT-4o mini
1) **End behavior of the graph**: The graph has a negative slope, indicating that as time (x) increases, the quantity of chips in the bag (y) decreases. Because the equation is linear and represents a situation where chips are consumed over time, the end behavior shows that as time approaches infinity, the quantity of chips approaches zero (y approaches 0).
2) **Reasonable domain for this scenario**: Given that the scenario involves a physical quantity (chips in a bag) decreasing over time, a reasonable domain would be all non-negative values of time. Thus, the domain could be \( x \geq 0 \), possibly up to the point when all chips are consumed, which is \( x \leq 7 \) (since the graph shows that after 7 minutes, there are no chips left). Therefore, a reasonable domain is \( [0, 7] \).
3) **Reasonable outputs for the scenario domain**: The outputs (amount of chips in oz., y) must correspond to the total amount of chips that can be in the bag at any given time from the domain identified.
- At \( x = 0 \) minutes, \( y = 3.5 \) oz.
- At \( x = 7 \) minutes, \( y = 0 \) oz.
Given the linear relationship and the endpoints, the reasonable outputs (y-values) would range from 0 to 3.5 oz., specifically \( y \in [0, 3.5] \).
2) **Reasonable domain for this scenario**: Given that the scenario involves a physical quantity (chips in a bag) decreasing over time, a reasonable domain would be all non-negative values of time. Thus, the domain could be \( x \geq 0 \), possibly up to the point when all chips are consumed, which is \( x \leq 7 \) (since the graph shows that after 7 minutes, there are no chips left). Therefore, a reasonable domain is \( [0, 7] \).
3) **Reasonable outputs for the scenario domain**: The outputs (amount of chips in oz., y) must correspond to the total amount of chips that can be in the bag at any given time from the domain identified.
- At \( x = 0 \) minutes, \( y = 3.5 \) oz.
- At \( x = 7 \) minutes, \( y = 0 \) oz.
Given the linear relationship and the endpoints, the reasonable outputs (y-values) would range from 0 to 3.5 oz., specifically \( y \in [0, 3.5] \).