 Define the function y = |x - 1| + 4
def f(x):
    return np.abs(x - 1) + 4

# Generate y values
y = f(x)

# Create the plot
plt.figure(figsize=(6,6))
plt.plot(x, y, label=r'$y = |x - 1| + 4$', color='b')

# Highlight the vertex and intercepts
plt.scatter(1, 4, color='red', zorder=5, label="Vertex (1, 4)")

# Labels and title
plt.axhline(0, color='black',linewidth=1)
plt.axvline(0, color='black',linewidth=1)
plt.xlim(-10, 10)
plt.ylim(-5, 15)
plt.title(r'Graph of $y = |x - 1| + 4$')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()

# Show the plot
plt.grid(True)
plt.show()Here is the graph of the function $ y = |x - 1| + 4 $. Key points to observe:

- The **vertex** is at $ (1, 4) $, which is the lowest point of the "V" shape.
- The graph is shifted **1 unit to the right** and **4 units up** compared to the basic absolute value function $ y = |x| $.
- The graph opens upwards with a slope of 1 for \( x >

Explore the graph of the absolute value function y = |x - 1| + 4. Learn how to graph absolute value functions, identify key points such as the vertex, and understand transformations including shifts. This problem is suitable for students in Grades 7-9.

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