Math Problem Statement

when is the function decreasing? give me the intervals from start to end

When is the function decreasing? Give me the intervals from start to end.

Solution

The graph you provided represents a function that starts from a point and slopes downward. From visual inspection, the function decreases as it moves from left to right.

To find the intervals where the function is decreasing:

  1. The function begins decreasing at x=3x = -3 and continues until it reaches x=3x = 3.
  2. The function is decreasing over the interval (3,3)(-3, 3).

Hence, the interval of decrease is: (3,3)(-3, 3).

Would you like to know more details about the function or any other related questions? Here are some to consider:

  1. How to find intervals where a function is increasing or decreasing.
  2. What is the slope of the function in the decreasing interval?
  3. How can you determine the domain and range from the graph?
  4. How do you identify the type of function from its graph?
  5. What is the significance of the slope in relation to the function's behavior?

Tip: For linear functions, the slope determines whether the function is increasing or decreasing. If the slope is negative, the function is decreasing.

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Math Problem Analysis

Mathematical Concepts

Functions
Decreasing Intervals
Graph Analysis

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

If the slope of a line is negative, the function is decreasing.

Suitable Grade Level

Grades 8-10