Let me analyze the image to determine the intervals for the function's increasing and decreasing behavior. PIL import Image import pytesseract

Load the image to process

image_path = '/mnt/data/173402143347090amoa0d.jpg' img = Image.open(image_path)

Use OCR to extract text (if relevant) and inspect the image visually

text = pytesseract.image_to_string(img) textThe image contains the question text, but to determine the intervals where the function is increasing or decreasing, I will visually analyze the graph in the image. Let me carefully examine it and provide the intervals based on what I observe.From the graph provided in the image, the intervals where the function is increasing and decreasing are determined by the slopes of the curve. Here's the breakdown:

Observations from the graph:

1. Increasing Intervals: The function is increasing (positive slope) where the graph moves upwards as $x$ increases.
2. Decreasing Intervals: The function is decreasing (negative slope) where the graph moves downwards as $x$ increases.

Solutions:

• Function is increasing on the intervals: $(-\infty, -2) \cup (0, 2)$

• Function is decreasing on the intervals: $(-2, 0) \cup (2, \infty)$

These intervals are derived based on the turning points observed at $x = -2, 0,$ and $2$.

Would you like a detailed explanation on how to read these intervals from a graph? Here are 5 related questions you can explore:

1. How do you determine critical points from a graph?
2. What role does the derivative play in finding increasing and decreasing intervals?
3. How do you write intervals using proper interval notation?
4. Can you explain how the behavior of the graph changes at turning points?
5. What are the practical applications of identifying increasing and decreasing intervals?

Tip: When analyzing a graph, look for where the slope changes from positive to negative or vice versa—it indicates a turning point!