GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsMedium
A production line's efficiency (E), in units per hour, is modeled by the function E(t) = -t² + 14t - 24, where t is the number of hours the line has been running since midnight (0 ≤ t ≤ 10). What is the practical domain for this function in the given context?
- AE(t) ≥ 0
- B0 ≤ t ≤ 10
- Ct ≥ 0
- DAll real numbers
Show answer & explanationAnswer & explanation
Correct answer: B. 0 ≤ t ≤ 10
The practical domain refers to the set of all possible input values (t) that make sense in the context of the problem. The problem explicitly states that t is the number of hours since midnight, with a range of 0 to 10 hours.
Why the other options are wrong
- A. This describes the range of the function (efficiency), not the domain (time).
- C. This only represents the lower bound of time, not the upper bound given in the problem.
- D. The mathematical domain of a quadratic is all real numbers, but the practical domain is restricted by the context.
Practical Domain of a Function
The practical domain of a function is the set of all input values (x or t) for which the function is defined and makes sense in the context of a real-world problem.
- Restricted by physical constraints (e.g., time cannot be negative).
- Restricted by problem statements (e.g., 'during the first 10 hours').
- Often a subset of the mathematical domain.
- Must result in meaningful output values.
Memory trick: Real-world Rules, not just Math's Tools!