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A rational function models the concentration of a medication, in milligrams per liter, t hours after a dose. The graph has a horizontal asymptote at y = 0 and a removable discontinuity at t = 2. Explain what each feature means in context and identify one reasonable domain restriction for the model.
Rubric
Setup · 1 pt
Defines a useful function, variable, or representation.
Features · 2 pt
Identifies and interprets key function features accurately.
Calculation · 1 pt
Performs appropriate algebraic or calculator-supported work.
Justification · 1 pt
Explains why the result follows from the model.
Context · 1 pt
Communicates units, constraints, or meaning in context.
Self-Score Response
Self-score: 0/6
Calibration Samples
The horizontal asymptote y = 0 means the medication concentration approaches 0 mg/L as time gets large, so the drug eventually leaves the bloodstream. A removable discontinuity at t = 2 means the formula has an undefined value there, but the modeled trend has a limiting concentration that could be estimated. A reasonable domain is t >= 0, since negative time after a dose is not meaningful.
The asymptote means the concentration gets close to zero. The hole means there is a missing point at 2 hours. The domain should be positive time.