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  # Adjusting the graph to a proper 1-5 range for x and y axes

# Define the x-values to range from 1 to 5
x_vals = np.linspace(1, 5, 400)

# Adjust the corresponding y-values for each equation
y1_vals = 5 - 2*x_vals  # y = 5 - 2x
y2_vals = 5 - 2*x_vals**2  # y = 5 - 2x²
y3_vals = 3*x_vals**2  # y = 3x²
y4_positive_vals = np.sqrt(5 - 2*x_vals**2)  # y² = 5 - 2x² (positive part)
y4_negative_vals = -np.sqrt(5 - 2*x_vals**2)  # y² = 5 - 2x² (negative part)
y5_vals = np.abs(5 - 9*x_vals)  # y = |5 - 9x|

# Set up the figure and axis, with both axes going from 1 to 5
fig, ax = plt.subplots(figsize=(8, 8))

# Plot the equations in the 1-5 range
ax.plot(x_vals, y1_vals, label="1. y = 5 - 2x", color="blue")
ax.plot(x_vals, y2_vals, label="2. y = 5 - 2x²", color="green")
ax.plot(x_vals, y3_vals, label="3. y = 3x²", color="red")
ax.plot(x_vals, y4_positive_vals, label="4. y² = 5 - 2x² (positive)", color="purple")
ax.plot(x_vals, y4_negative_vals, label="4. y² = 5 - 2x² (negative)", color="purple", linestyle="--")
ax.plot(x_vals, y5_vals, label="5. y = |5 - 9x|", color="orange")

# Set the axis limits to 1-5 for both x and y
ax.set_xlim(1, 5)
ax.set_ylim(1, 5)

# Add grid, x and y axis labels
ax.axhline(0, color='black',linewidth=1)
ax.axvline(0, color='black',linewidth=1)
ax.set_xlabel("x")
ax.set_ylabel("y")

# Add a title and legend
ax.set_title("Graphs of Equations 1-5 in x and y range from 1 to 5")
ax.legend()

# Show the plot
plt.show()