https://file.aiquickdraw.com/mathbot/file/1731862060824ojr46rzb.jpg

from PIL import Image
import pytesseract

# Load the image to process it
image_path = '/mnt/data/1731862060824ojr46rzb.jpg'
extracted_text = pytesseract.image_to_string(Image.open(image_path))

extracted_text'Graph the following function on the axes provided.\n\nf(a) —x—5 for x2<-—A4\nZz =\n5a —23 for «z>5\n''Graph the following function on the axes provided.\n\nf(a) —x—5 for x2<-—A4\nZz =\n5a —23 for «z>5\n'successThe extracted text has some errors due to the clarity of the image. Based on the visual interpretation and extracted information:

The function to graph is:
\[
f(x) = 
\begin{cases} 
-x - 5 & \text{for } x \leq -4 \\
5x - 23 & \text{for } x > 5 
\end{cases}
\]

I will plot this piecewise function for you.import numpy as np
import matplotlib.pyplot as plt

# Define the piecewise function
def f(x):
    return np.where(x <= -4, -x - 5, np.where(x > 5, 5*x - 23, np.nan))

# Define the x values for plotting
x1 = np.linspace(-10, -4, 100)  # For the first piece
x2 = np.linspace(5, 10, 100)   # For the second piece

# Calculate y values for each piece
y1 = f(x1)
y2 = f(x2)

# Plot the function
plt.figure(figsize=(8, 6))
plt.plot(x1, y1, label=r"$f(x) = -x - 5$ for $x \leq -4$", color='blue')
plt.plot(x2, y2, label=r"$f(x) = 5x - 23$ for $x > 5$", color='green')

# Add additional plot details
plt.axhline(0, color='black', linewidth=0.5, linestyle='--')
plt.axvline(0, color='black', linewidth=0.5, linestyle='--')
plt.title("Graph of the Piecewise Function")
plt.xlabel("x")
plt.ylabel("f(x)")
plt.legend()
plt.grid()
plt.show()
<<ImageDisplayed>>successHere is the graph of the given piecewise function. It shows:

1. The first part, $f(x) = -x - 5$, for $x \leq -4$, plotted as a blue line.
2. The second part, $f(x) = 5x - 23$, for $x > 5$, plotted as a green line.

Would you like to explore this graph further or have any questions about it?

### Related Questions:
1. What happens to $f(x)$ at $x = -4$ and $x = 5$?
2. How do we evaluate continuity at the boundaries of piecewise functions?
3. Can you calculate the slope for each piece of the function?
4. How would the graph look if we added another piece for $-4 < x \leq 5$?
5. What are the y-intercepts of the given linear pieces?

### Tip:
When sketching piecewise functions, always check the values and slopes at the boundaries to understand their behavior better.

Graph the following function on the axes provided.

f(x) =
   -x - 5  for x <= -4
   5x - 23 for x > 5

Explore the graph of a piecewise function where f(x) = -x - 5 for x ≤ -4 and f(x) = 5x - 23 for x > 5. This step-by-step guide shows how to plot linear equations on separate intervals and analyze their behavior.

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