Math Problem Statement

On what x-interval is the graph decreasing?

Solution

To determine the x-interval on which the graph is decreasing, we analyze the graph's slope:

  1. From the left side, the graph starts from a point around (6,6)(-6, -6) and increases until it reaches its maximum point at (2,10)(2, 10).
  2. After reaching the peak at (2,10)(2, 10), the graph starts decreasing as the slope becomes negative, continuing down until (6,2)(6, -2).

Thus, the graph is decreasing between the x-values 22 and 66, meaning the correct answer is:

Option: (2, 6)

Would you like more details or further explanations?


Here are 5 questions to expand on this topic:

  1. What does it mean for a graph to be increasing or decreasing?
  2. How can the slope of a line indicate whether the graph is increasing or decreasing?
  3. What is the significance of a graph’s maximum and minimum points?
  4. How can we determine intervals of increase and decrease algebraically?
  5. How do changes in the slope affect the shape of the graph?

Tip: The slope of a line segment on a graph tells you whether the graph is increasing (positive slope) or decreasing (negative slope).

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Math Problem Analysis

Mathematical Concepts

Graph Analysis
Functions
Intervals of Increase and Decrease

Formulas

None (graph interpretation)

Theorems

First Derivative Test (in calculus, for general context)

Suitable Grade Level

Grades 7-9