Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions, showing key features by hand in simple cases and with technology when the functions are more complicated.
Translate a context into an exact piecewise graph record
Problem
Translate the fee schedule into an exact graph record for cost \(C\) versus hours \(h\). Write each constant rule on its interval, assign open and closed endpoints at \(h=0,2,5\), determine \(C(2)\), and state the domain, range, and values at \(h=1\) and \(h=3\).
A contextual piecewise graph starts by naming the input and output with units. We’ll translate each fee band into a rule and interval, turn threshold wording into open or closed endpoints, and check the combined domain, range, and representative values.
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