GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsHard
A nutritionist is tracking a patient's weight loss. The patient's weight, W (in pounds), over time, t (in weeks), is modeled by the function W(t) = -2.5t + 220. What is the practical range of this function for a 20-week program, assuming the patient starts at 220 pounds and cannot weigh less than 100 pounds?
- AW(t) ≥ 100
- B100 ≤ W(t) ≤ 220
- C0 ≤ t ≤ 20
- DW(t) ≤ 220
Show answer & explanationAnswer & explanation
Correct answer: B. 100 ≤ W(t) ≤ 220
The practical range is the set of all possible output values (weight) that make sense in the context of the problem. We need to consider the starting weight, the minimum allowed weight, and the weight after 20 weeks. The patient starts at 220 pounds (maximum weight). After 20 weeks, W(20) = -2.5(20) + 220 = -50 + 220 = 170 pounds. The minimum allowed is 100 pounds. So the range is between 100 and 220, inclusive.
Why the other options are wrong
- A. This only represents the lower bound and implies weight can go infinitely high.
- C. This describes the practical domain (time), not the practical range (weight).
- D. This only represents the upper bound and implies weight can go infinitely low.
Practical Range of a Function
The practical range of a function is the set of all output values (y or W(t)) that are realistic and meaningful within the context of a real-world problem, considering both the function's behavior and external constraints.
- Dependent on the practical domain.
- Restricted by physical constraints (e.g., non-negative quantities).
- Limited by explicit problem conditions (e.g., 'cannot weigh less than X').
- Often involves evaluating the function at the boundaries of the practical domain.
Memory trick: Output Limits, Real-World Fits!