Math Problem Statement

Determine if each of the following intervals is increasing, decreasing or constant: (-10, -5) and (0, 5)

Solution

The graph provided has several line segments, and we need to determine whether the function is increasing, decreasing, or constant over the specified intervals.

Analysis of the Intervals:

  1. Interval (-10, -5):
    In this interval, the line segment is sloping downwards, meaning that the function is decreasing.

  2. Interval (0, 5):
    In this interval, the line segment is horizontal, which means the function remains constant (no increase or decrease).

Conclusion:

  • For the interval (10,5)(-10, -5), the function is decreasing.
  • For the interval (0,5)(0, 5), the function is constant.

Would you like more details or have any questions?

Here are 5 related questions to consider:

  1. How can you determine the slope of a line segment from a graph?
  2. What is the significance of the slope in identifying whether a function is increasing or decreasing?
  3. How do you describe a function that is constant over a specific interval?
  4. What are the other intervals in the graph, and how do they behave?
  5. How does the function behave as it approaches x=0x = 0?

Tip: When analyzing the behavior of a function over an interval, look at the slope of the line segment within that interval. A positive slope indicates an increase, a negative slope indicates a decrease, and a zero slope indicates a constant function.

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Math Problem Analysis

Mathematical Concepts

Graph Analysis
Slope
Intervals

Formulas

Slope formula: (change in y) / (change in x)

Theorems

Slope and Behavior Theorem

Suitable Grade Level

Grades 9-11