Build a function from context by determining an explicit formula, recursive rule, or calculation process.
Build a piecewise function from a tiered context
Problem
Parking costs \(\$5\) for up to the first hour and \(\$2\) for each additional hour. Let \(h\) be total hours parked. Write a piecewise function for the cost.
Big Picture
What this problem is really about
A tiered price needs one rule for each interval where the calculation changes. We’ll locate the time boundary, assign it to exactly one piece, and distinguish total hours from only the hours beyond that boundary. The later rule must retain the earlier flat charge before adding the extra-hour cost, and boundary checks guard against gaps or overlap.
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