Math Problem Statement
Solution
The image shows a graph with related questions asking to solve inequalities and write solution sets in interval notation. Let me analyze the graph and assist you in solving each part.
Analyzing the Graph:
The graph appears to show intervals where is positive, negative, or zero. Key points include where the curve crosses the x-axis, as this helps determine intervals for each inequality.
(a) :
This represents where the graph is below the x-axis.
- From the graph, on:
- and .
Solution Set: .
(b) :
This includes where is negative or zero (touching the x-axis).
- From the graph, on:
- and .
Solution Set: .
(c) :
This represents where the graph is above the x-axis.
- From the graph, on:
- and .
Solution Set: .
(d) :
This includes where is positive or zero.
- From the graph, on:
- and .
Solution Set: .
Would you like a detailed explanation of how I derived these intervals? Let me know!
Related Questions:
- How do you determine the intervals where a function is positive or negative?
- What is the significance of using brackets () vs. parentheses () in interval notation?
- How do we check the behavior of a function around critical points like ?
- What changes if the inequality includes or excludes the equals sign ()?
- Can you explain how to solve such inequalities algebraically if given explicitly?
Tip: Always check the graph thoroughly for key points where , as these divide the intervals for inequalities.
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Math Problem Analysis
Mathematical Concepts
Graph Analysis
Inequalities
Interval Notation
Formulas
Understanding interval notation to represent solutions.
Theorems
Basic principles of graph-based inequality solutions.
Suitable Grade Level
Grades 9-12
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