Annotations, Reference Lines & Legends

The problem, from first principles

A chart that only shows lines makes the reader do the work. The good ones point: an arrow at the peak with its value, a dashed line at the target, a shaded band over the period that mattered, a legend that says which colour is which. These extras are cheap to add and are what turn a plot from "data" into "an argument". They are also objects, Annotation, Line2D and Polygon patches, with positions and text you can read back.

This question builds four such touches: an annotated maximum, a horizontal threshold with a label, a shaded span between two x values, and a legend placed outside the plot area so it never hides data.

From theory to code

Implement annotate_max(ax, x, y), add_threshold(ax, value, label), shade_region(ax, x0, x1, label) and legend_below(ax, title). The signatures and docstrings are already in the editor.

Constraints

• annotate_max(ax, x, y) finds the point with the largest y (the first one if tied) and adds an annotation whose text is f"max = {y_max:g}", which points at (x_max, y_max) with an arrow, with its text placed 20 points above that point (xytext=(0, 20), textcoords="offset points"). It returns the Annotation.
• add_threshold(ax, value, label) draws a horizontal line at y = value, colour "gray", linestyle "--", with that label, shows the legend, and returns the line.
• shade_region(ax, x0, x1, label) shades the vertical band between x0 and x1 with colour "orange" and alpha=0.2 and the given label, and returns the patch.
• legend_below(ax, title) shows the legend with that title, centred under the axes (loc="upper center", bbox_to_anchor=(0.5, -0.15)) in two columns, and returns the Legend.
• x and y are equal-length numeric sequences. Do not call plt.show().

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