Math Problem Statement

Determine the interval(s) on which the function is (strictly) decreasing. 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 problem asks to determine the interval(s) where the given function is strictly decreasing. Here's how we approach this:

  1. Inspect the Graph: Look at the segments of the function to identify where the function decreases (i.e., as xx increases, yy decreases).

From the graph:

  • The function decreases in the interval (5,3)(-5, -3) and also in the interval (0,2)(0, 2).
  1. Write the Answer:
  • Combine the intervals of decrease: (5,3),(0,2)(-5, -3), (0, 2).

Let me know if you need further clarification or detailed steps on how I identified these intervals.


Related Questions:

  1. What does it mean for a function to be "strictly decreasing" versus "decreasing"?
  2. How do you describe the behavior of a function in terms of increasing and decreasing intervals?
  3. Can a function be both increasing and decreasing at a specific xx-value?
  4. How does differentiability relate to increasing or decreasing intervals of a function?
  5. What tools can you use to find decreasing intervals algebraically without a graph?

Tip: Always look for segments where the slope is negative (function decreases) and describe them using open intervals where applicable.

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Math Problem Analysis

Mathematical Concepts

Graph Interpretation
Function Behavior Analysis

Formulas

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Theorems

Definition of strictly decreasing functions

Suitable Grade Level

Grades 9-12