https://file.aiquickdraw.com/mathbot/file/1726506830122hxecikt0.jpg

find the range decreasing and increasing 

From the image, the graph is a continuous curve with alternating increasing and decreasing sections. Let's break this down:

### 1. **Range**:
   The range of a function refers to all the possible values of \( y \) (output). Looking at the graph:
   - The highest point on the graph seems to be at \( y = 3 \).
   - The lowest point on the graph appears to be \( y = -3 \).
   
   Therefore, the **range** of the function is:
   \[
   \boxed{[-3, 3]}
   \]

### 2. **Intervals of Increase**:
   A function is increasing where the graph rises as you move from left to right. In this case, the function increases in two intervals:
   - From \( x = -4 \) to \( x = -2 \) (the graph moves upwards in this range).
   - From \( x = 0 \) to \( x = 2 \).

   Therefore, the intervals of increase are:
   \[
   \boxed{(-4, -2)} \text{ and } \boxed{(0, 2)}
   \]

### 3. **Intervals of Decrease**:
   A function is decreasing where the graph falls as you move from left to right. The graph decreases in these intervals:
   - From \( x = -2 \) to \( x = 0 \) (the graph moves downwards here).
   - From \( x = 2 \) to \( x = 4 \).

   Therefore, the intervals of decrease are:
   \[
   \boxed{(-2, 0)} \text{ and } \boxed{(2, 4)}
   \]

Would you like a more detailed explanation of how to determine increasing and decreasing intervals? 

Here are five related questions you can explore:
1. How do you find the domain of a function from its graph?
2. What are local maxima and minima, and where are they in this graph?
3. Can you explain how to identify points of inflection from a graph?
4. How do derivatives relate to increasing and decreasing functions?
5. What is the importance of critical points in determining increasing or decreasing behavior?

**Tip:** When analyzing graphs, always check for key points like turning points (maxima and minima) to determine where the graph changes direction!

Find the range, increasing, and decreasing intervals for the given graph.

Learn how to determine the range, and the increasing and decreasing intervals of a function from its graph. This problem covers key graph analysis concepts, including intervals of increase and decrease, and the function's range. Suitable for students in Grades 9-12.

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