Question 6 of 10 The water was pumped out of a backyard pond. What is the domain of this graph? Depth (inches) A. All real numbers B.
C.
D.
Water Depth 110 100 90 80 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 8 9 10 11 Time (minutes)
The Correct Answer and Explanation is:
The correct answer is:
D. 0≤x≤80 \leq x \leq 8
Explanation:
In mathematics, the domain of a graph refers to the set of all possible input values (in this case, time in minutes) for which the function is defined.
Step-by-Step Analysis:
- Context of the Problem:
- The question discusses a situation where water is being pumped out of a backyard pond.
- The graph shows water depth (in inches) on the vertical axis and time (in minutes) on the horizontal axis.
- Reading the Graph:
- At time x=0x = 0, the water depth is at its maximum, around 100 inches.
- As time increases, the water depth decreases linearly.
- The graph stops at x=8x = 8, where the depth reaches 0 inches — meaning the pond is completely empty after 8 minutes.
- What is the Domain?
- The domain is the range of time values for which the depth is defined or meaningful.
- The pump starts at minute 0 and finishes by minute 8.
- There is no data before 0 minutes (negative time doesn’t make sense in this context) and no water depth beyond 8 minutes since the pond is empty.
- Therefore, the domain is from x=0x = 0 to x=8x = 8, inclusive.
- Why Not Other Choices?
- A. All real numbers: Incorrect. You cannot have negative time or pump water beyond when the pond is empty.
- B. 0≤x≤950 \leq x \leq 95: Incorrect. The graph ends at 8 minutes, not 95.
- C. x≥0x \geq 0: Incorrect. This implies the graph continues forever, but it ends at 8 minutes.
Conclusion:
The water was pumped out in a finite amount of time, from 0 to 8 minutes. Therefore, the domain of the graph — the set of all time values during which the water depth is defined — is:
0≤x≤80 \leq x \leq 8
Answer: D.
