Math Problem Statement
Graph the following function on the axes provided.
f(x) =
-x - 5 for x <= -4
5x - 23 for x > 5
Solution
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:
\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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Graphing Linear Functions
Formulas
f(x) = -x - 5
f(x) = 5x - 23
Theorems
Linear equations and their graphical representation
Suitable Grade Level
Grades 9-11