Math Problem Statement

Determine all intervals on which the graph of f is decreasing.

Solution

The problem asks us to determine the intervals where the graph of the function ff is decreasing.

From the image, we can identify the intervals where the graph of ff is decreasing by observing the segments of the graph that are sloping downwards (moving from left to right).

Here are the decreasing intervals:

  1. The graph decreases from approximately x=3x = -3 to x=1x = -1.
  2. It decreases again from approximately x=1x = 1 to x=3x = 3.

Thus, the intervals where the graph of ff is decreasing are: (3,1)(1,3)(-3, -1) \cup (1, 3)

Would you like further details on how to interpret the graph or analyze other properties?

Here are five related questions to deepen your understanding:

  1. What are the intervals where the graph of ff is increasing?
  2. Can you identify the local maxima and minima on this graph?
  3. How can you determine the concavity of the graph?
  4. What is the significance of the x-intercepts in the context of this graph

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Math Problem Analysis

Mathematical Concepts

Calculus
Functions
Intervals
Decreasing Functions

Formulas

-

Theorems

Monotonicity Theorem

Suitable Grade Level

Grades 10-12