Math Problem Statement

Determine the interval(s) on which the function is constant. Write your answer as an interval or list of intervals. When writing a list of intervals, make sure to separate each interval with a comma and to use as few intervals as possible.

Solution

The task asks to determine the interval(s) where the function is constant based on the graph shown.

From the graph, let's analyze the intervals:

  • The graph is increasing or decreasing in most regions, but there are two segments where the function is constant:
    • One segment occurs from x=2x = -2 to x=0x = 0. In this interval, the function is a horizontal line, indicating a constant value.
    • Another constant interval is between x=2x = 2 and x=3x = 3.

Thus, the function is constant on the intervals: [ [-2, 0] \quad \text{and} \quad [2, 3] ]

Make sure to input the intervals with a comma between them, like this: [-2, 0], [2, 3].

Would you like further clarification or details on this? Here are some additional related questions:

  1. What does it mean for a function to be constant over an interval?
  2. How can you determine if a function is increasing or decreasing from a graph?
  3. What are the key differences between constant and non-constant intervals?
  4. How does the slope of a line relate to whether a function is constant?
  5. Can a function have multiple constant intervals?

Tip: Always check the graph carefully to see if any portion of the function remains flat—this indicates a constant interval.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Intervals
Graph Interpretation

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10