From 3a5e41315072350a1208d16c4afeb86612af21d1 Mon Sep 17 00:00:00 2001
From: zimmersandro <sandro.zimmermann@stud.fhgr.ch>
Date: Mon, 26 Oct 2026 14:06:52 +0100
Subject: [PATCH] Serie 5 Aufgabe 3. Jedes plot hat eine unterschiedliche
 Linienfarbe und eine Legende mit der Funktion als Beschreibung

---
 reelle_funktionen/serie_5_3.py | 70 +++++++++++++++++++++++++++++-----
 1 file changed, 61 insertions(+), 9 deletions(-)

diff --git a/reelle_funktionen/serie_5_3.py b/reelle_funktionen/serie_5_3.py
index de3fbd3..72ddc23 100644
--- a/reelle_funktionen/serie_5_3.py
+++ b/reelle_funktionen/serie_5_3.py
@@ -1,57 +1,109 @@
 #%%
-import numpy as np
-import matplotlib.pyplot as plt
+# Import required libraries
+import numpy as np          # Numerical operations and array handling
+import matplotlib.pyplot as plt  # Plotting library
 
+# Initialize figure counter and line width for all plots
 fig = 0
 lw = 3
 
-functions = [
+# Named color palette mapping descriptive names to hex codes
+colors = {
+    "deep blue": "#1f77b4",
+    "orange": "#ff7f0e",
+    "green": "#2ca02c",
+    "red": "#d62728",
+    "purple": "#9467bd",
+    "brown": "#8c564b",
+}
+
+# List of functions to plot, each with its domain, resolution, callable,
+# LaTeX label, and assigned color
+plots = [
     {
         "x_0": 0.,
         "x_E": 2.,
         "N": 2,
         "f": lambda x: 0.4 * x + 1,
+        "label": r"$f(x) = 0.4\,x + 1$",
+        "color": colors["deep blue"],
     },
     {
         "x_0": -2.,
         "x_E": 2.,
         "N": 129,
         "f": lambda x: x ** 2,
+        "label": r"$f(x) = x^2$",
+        "color": colors["orange"],
     },
     {
         "x_0": -6.,
         "x_E": 2.,
         "N": 129,
         "f": lambda x: 2 ** x,
+        "label": r"$f(x) = 2^x$",
+        "color": colors["green"],
     },
     {
         "x_0": 0.01,
         "x_E": 10.,
         "N": 129,
-        "f": lambda x: np.log(x)/np.log(10),
+        "f": lambda x: np.log(x) / np.log(10),
+        "label": r"$f(x) = \log_{10}(x)$",
+        "color": colors["red"],
     },
     {
         "x_0": -1,
         "x_E": 4,
         "N": 129,
         "f": lambda x: 3 / (x + 2),
+        "label": r"$f(x) = \dfrac{3}{x+2}$",
+        "color": colors["purple"],
     },
     {
         "x_0": 0,
         "x_E": 4 * np.pi,
         "N": 257,
         "f": lambda x: 2 * np.sin(x),
+        "label": r"$f(x) = 2\,\sin(x)$",
+        "color": colors["brown"],
     },
 ]
 
-for function in functions:
-    x_data = np.linspace(function["x_0"], function["x_E"], function["N"])
-    y_data = function["f"](x_data)
+# Loop over each plot definition and create a separate figure
+for plot in plots:
+    # Generate evenly spaced x values over the specified domain
+    x_data = np.linspace(plot["x_0"], plot["x_E"], plot["N"])
 
+
+    # Evaluate the function at each x point
+    y_data = plot["f"](x_data)
+
+    # Create a new figure for the current plot
     fh = plt.figure(fig)
     fig += 1
-    plt.plot(x_data, y_data, linewidth=lw)
+
+    # Plot the curve with the assigned color, line width, and LaTeX label
+    plt.plot(
+        x_data,
+        y_data,
+        linewidth=lw,
+        color=plot["color"],
+        label=plot["label"],
+    )
+
+    # Set axis labels
     plt.xlabel(r"$x$")
     plt.ylabel(r"$y$")
+
+    # Display a grid for readability
     plt.grid(visible=True)
-    plt.axis("image")
\ No newline at end of file
+
+    # Enforce equal scaling on both axes
+    plt.axis("image")
+
+    # Add a legend showing the function expression in LaTeX
+    plt.legend()
+
+# Display all figures
+plt.show()
\ No newline at end of file