Math Problem Statement
Solution
To determine the domain on which the function is decreasing, we need to analyze the behavior of the graph. A function is decreasing when the y-values (vertical) are getting smaller as the x-values (horizontal) increase.
From the graph, it appears that the function increases until it reaches a maximum point and then starts to decrease. Let’s identify these points:
- Increasing interval: The graph increases from around to .
- Decreasing interval: After the function reaches its peak at , it starts decreasing from to , where the function hits the x-axis.
Thus, the domain on which the function is decreasing is the interval:
This is the domain where the function's slope is negative.
Would you like more details or have any questions?
Here are some additional related questions for practice:
- What is the maximum value of the function and at what point does it occur?
- On what interval is the function increasing?
- Can you determine the function's intercepts?
- What is the range of the function based on the graph?
- How would you calculate the slope at different intervals using the graph?
Tip: Always look for the peak or turning point of a graph when determining where a function is decreasing!
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Math Problem Analysis
Mathematical Concepts
Graph Analysis
Functions
Intervals of Increase and Decrease
Formulas
-
Theorems
Decreasing Function Theorem
Suitable Grade Level
Grades 9-12
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