Evaluate a Piecewise Linear Function

You are given an ordered list of 2D points [(x1, y1), (x2, y2), ..., (xn, yn)]. Connecting each consecutive pair of points forms a piecewise linear function.

Given a target value target_x, return the corresponding y value on the function at that x-coordinate.

Assume:

• The points are ordered by increasing x .
• The function is defined by straight-line interpolation between consecutive points.
• target_x may coincide with an existing point or fall between two adjacent points.

Clarify how you would handle edge cases such as:

• target_x outside the covered x-range
• duplicate x-values
• invalid input with fewer than 2 points

Example:

• Points: [(1, 2), (3, 6), (5, 4)]
• target_x = 2
• Output: 4 , because the point lies on the line segment between (1, 2) and (3, 6) .