Math Problem Statement

Determine the domain on which the following function is decreasing.

Solution

To determine the domain on which the function is decreasing, we need to analyze the behavior of the graph. A function is decreasing when the y-values (vertical) are getting smaller as the x-values (horizontal) increase.

From the graph, it appears that the function increases until it reaches a maximum point and then starts to decrease. Let’s identify these points:

  1. Increasing interval: The graph increases from around x=0x = 0 to x=6x = 6.
  2. Decreasing interval: After the function reaches its peak at x=6x = 6, it starts decreasing from x=6x = 6 to x=14x = 14, where the function hits the x-axis.

Thus, the domain on which the function is decreasing is the interval: (6,14)\boxed{(6, 14)}

This is the domain where the function's slope is negative.

Would you like more details or have any questions?

Here are some additional related questions for practice:

  1. What is the maximum value of the function and at what point does it occur?
  2. On what interval is the function increasing?
  3. Can you determine the function's intercepts?
  4. What is the range of the function based on the graph?
  5. How would you calculate the slope at different intervals using the graph?

Tip: Always look for the peak or turning point of a graph when determining where a function is decreasing!

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Math Problem Analysis

Mathematical Concepts

Graph Analysis
Functions
Intervals of Increase and Decrease

Formulas

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Theorems

Decreasing Function Theorem

Suitable Grade Level

Grades 9-12