Math Problem Statement
Solution
To determine over what intervals the function in the graph is negative, we need to observe where the curve lies below the x-axis (where ).
From the graph:
- The function crosses the x-axis at points approximately and .
- The function is negative (below the x-axis) between and .
Thus, the correct interval where the function is negative is .
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Here are 5 relative questions to further explore this topic:
- What is the significance of the points where the function crosses the x-axis?
- How do we determine whether a function is positive or negative in specific intervals?
- How can we describe the behavior of the function in intervals where it does not cross the x-axis?
- What role do critical points play in understanding a function's graph?
- How can we analyze concavity based on the graph of a function?
Tip: Always check the behavior of a function at critical points and where it crosses the axes, as these points often give valuable information about the function's behavior across intervals.
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Math Problem Analysis
Mathematical Concepts
Graphing Functions
Intervals
Negative Function Values
Formulas
-
Theorems
Behavior of functions on intervals
Sign of function values
Suitable Grade Level
Grades 9-12
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