from PIL import Image import pytesseract

Load the image

img_path = '/mnt/data/1724822301536z0qcnvd4.jpg' img = Image.open(img_path)

Perform OCR to extract any text

text = pytesseract.image_to_string(img)

textThe text extraction from the image wasn't fully successful due to the handwriting and formatting. However, I can still analyze the piecewise function based on the graph you provided.

Let's examine the graph section by section:

1. For $-6 \leq x < -1$:

• The graph is a horizontal line at $y = 4$.
• This can be written as: $f(x) = 4$.

2. For $-1 \leq x \leq 2$:

• The graph shows a line with a negative slope, starting from $( -1, 4 )$ and ending at $( 2, -1 )$.
• The equation of this line can be found using the point-slope form: $\text{slope} = \frac{-1 - 4}{2 - (-1)} = \frac{-5}{3}$ So the equation is: $f(x) = -\frac{5}{3}x + \frac{7}{3}$

3. For $2 < x \leq 6$:

• The graph shows another line with a negative slope, starting from $(2, -1)$ and ending at $(6, -5)$.
• The slope is: $\text{slope} = \frac{-5 - (-1)}{6 - 2} = \frac{-4}{4} = -1$ So the equation is: $f(x) = -x + 1$

The piecewise function is:

\begin{cases} 4 & \text{if } -6 \leq x < -1 \\ -\frac{5}{3}x + \frac{7}{3} & \text{if } -1 \leq x \leq 2 \\ -x + 1 & \text{if } 2 < x \leq 6 \end{cases}$$ Let me know if you need more details or have any questions! Here are five related questions that could further your understanding: 1. How do you derive the equation of a line given two points? 2. What are the common types of piecewise functions? 3. How can you determine if a piecewise function is continuous? 4. What are the implications of the slope in a linear function? 5. How do you determine the range of a piecewise function based on its graph? **Tip:** When working with piecewise functions, carefully observe the open and closed endpoints as they indicate whether the point is included in the interval.