Math Problem Statement

Over what intervals is the function below negative?

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 y<0y < 0).

From the graph:

  • The function crosses the x-axis at points approximately x=3x = -3 and x=0x = 0.
  • The function is negative (below the x-axis) between x=3x = -3 and x=0x = 0.

Thus, the correct interval where the function is negative is (3,0)(-3, 0).

Let me know if you need any further details or have any questions!

Here are 5 relative questions to further explore this topic:

  1. What is the significance of the points where the function crosses the x-axis?
  2. How do we determine whether a function is positive or negative in specific intervals?
  3. How can we describe the behavior of the function in intervals where it does not cross the x-axis?
  4. What role do critical points play in understanding a function's graph?
  5. 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

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Theorems

Behavior of functions on intervals
Sign of function values

Suitable Grade Level

Grades 9-12