Math Problem Statement

Consider the following graph of a well-defined real function. Based on the graph, determine the number of intervals where the function is decreasing.

Solution

To determine the intervals where the function is decreasing based on the given graph, let's analyze it.

Looking at the graph, we observe that the function has the following decreasing segments:

  • From x=2x = -2 to x=0x = 0
  • From x=5x = 5 to x=7x = 7

These intervals show where the function is decreasing because the curve moves downward as we move from left to right.

Thus, the answer is: 2 intervals

Would you like to go over more details or have any further questions about this graph?

Here are 5 related questions:

  1. What are the intervals where the function is increasing?
  2. What is the function's behavior at the local maximum and minimum points?
  3. How can we find the critical points of a function from its graph?
  4. How do you determine whether a function is concave up or concave down?
  5. What is the difference between an increasing, decreasing, and constant function in terms of graph analysis?

Tip: Always look for peaks (local maxima) and valleys (local minima) on a graph when identifying intervals of increase or decrease.

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Math Problem Analysis

Mathematical Concepts

Graphing Functions
Intervals of Increase/Decrease
Real Functions

Formulas

Identifying Intervals of Increase/Decrease from a Graph

Theorems

Understanding the behavior of functions from graphical representations

Suitable Grade Level

Grades 9-11