Math Problem Statement
Solution
Let's go through each part of the problem.
Problem Overview:
You are given a graph of a function , where represents the depth of water in a reservoir days since the beginning of the year. The graph spans the interval .
(a) [2 marks] Domain and Range
-
Domain: This is the set of possible -values. From the graph, represents the number of days since the beginning of the year, and it is defined from to .
- Domain: .
-
Range: This is the set of possible -values, which represent the water depth. From the graph, the depth seems to vary between approximately and .
- Range: Approximately .
(b) [3 marks] Find and and Explain
-
From the graph:
- .
- .
These values represent the depth of the water in the reservoir on the 100th day and 200th day of the year.
(c) [1 mark] Find such that
- From the graph, appears to happen at two points:
- days.
- days.
(d) [2 marks] Intervals of Increase and Decrease
- Increasing: The function increases from day to about days.
- Decreasing: The function decreases from about days to days.
- Increasing again: The function increases slightly again from about to days.
Would you like further details or have any questions about the solution?
5 Additional Related Questions:
- What is the maximum depth of water in the reservoir according to the graph?
- Estimate the day when the depth of the water is the highest.
- How would you interpret the meaning of the decreasing intervals in terms of reservoir activity?
- Can you determine the average depth of the reservoir over the year based on the graph?
- How would you find the total amount of water in the reservoir over a period of time using this graph?
Tip:
When interpreting graphs, always pay attention to the units and labels on both axes. This will help provide accurate context for domain, range, and specific points.
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Math Problem Analysis
Mathematical Concepts
Graph Analysis
Functions
Domain and Range
Increasing and Decreasing Intervals
Formulas
None required for this problem; focuses on graph interpretation.
Theorems
None specific; applies graphical and interval analysis.
Suitable Grade Level
Grades 10-12
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