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 >