Question 178·Easy·Nonlinear Functions
The function models a studio’s total cost, in dollars, to produce custom T-shirts. What is the best interpretation of the statement in this context?
For function-interpretation questions, first identify clearly what the input and output represent in words (here: input = number of shirts, output = total cost). Then read a statement like as a single input–output pair: “when the input is 30, the output is 540,” and translate that directly into a sentence about the context. Finally, eliminate choices that incorrectly treat the output as a rate, a change, or a per-item cost instead of a single total amount.
Hints
Clarify inputs and outputs
Ask yourself: In this problem, what does the input stand for, and what does the output stand for?
Focus on
is the value of the cost function when . What real-world situation does “producing 30 shirts” describe?
Interpret the number 540
If is total cost, then the equation tells you the total cost for a specific number of shirts. Which choice describes a single total cost for 30 shirts, not a rate or a cost per shirt?
Step-by-step Explanation
Identify what the function represents
The problem says models the studio’s total cost, in dollars, to produce custom T‑shirts.
- The input = number of shirts.
- The output = total cost (not cost per shirt).
Interpret the notation
means we plug in , so we are talking about the situation when 30 shirts are produced.
- is the total cost when .
Use the equation
The equation tells us that the total cost corresponding to producing 30 shirts is $540.
- So, when 30 shirts are made, the studio spends $540 in total.
- This matches the interpretation: Producing 30 shirts will cost $540 in total.