GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A production manager is analyzing the cost of manufacturing a new product. The cost, C, in dollars, is a function of the number of units produced, x, and is given by the equation C(x) = 5x + 150. What is the practical domain of this function if the company can produce a minimum of 0 units and a maximum of 100 units?
- Ax ≥ 0
- B[150, 650]
- C(-∞, ∞)
- D[0, 100]
Show answer & explanationAnswer & explanation
Correct answer: D. [0, 100]
The practical domain represents the realistic input values for the number of units produced. Since the company can produce between 0 and 100 units, inclusive, the domain is the closed interval [0, 100].
Why the other options are wrong
- A. This represents all non-negative numbers, but does not include the upper limit of 100 units.
- B. This represents the practical range of the cost, not the domain (number of units).
- C. This represents all real numbers, which is not practical for units produced.
Practical Domain
The practical domain of a function represents the set of all realistic input values that make sense within the context of a real-world problem.
- Considers physical or practical limitations.
- Often restricted to non-negative numbers or specific ranges.
- Different from the mathematical domain, which includes all values for which the function is defined.
Memory trick: Real-world limits define the input road.