Math Problem Statement
increasing vs. decreasing & pos vs. neg (level 2)
Determine all intervals on which the graph of f is decreasing.
Solution
To determine where the function is decreasing, we need to identify the intervals on the -axis where the graph is sloping downwards as increases.
Looking at the graph, appears to be decreasing in the following intervals:
- From to , the graph slopes downward.
- From to , the graph also decreases.
Therefore, the intervals where the function is decreasing are:
Would you like further explanation on how to interpret these intervals or any other aspect?
Here are 5 related questions for further practice:
- How do you determine where a function is increasing on a graph?
- What is the significance of turning points in identifying increasing and decreasing intervals?
- How can you identify intervals of positive and negative values for ?
- How does the concept of the derivative relate to increasing and decreasing intervals?
- What is the role of concavity in understanding the behavior of a function's graph?
Tip: When analyzing graphs for increasing or decreasing behavior, always look for the slopes of the curve between critical points.
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Math Problem Analysis
Mathematical Concepts
Functions
Intervals
Increasing and Decreasing Functions
Formulas
-
Theorems
Concept of Decreasing Functions
Suitable Grade Level
Grades 10-12