A hardware store rents vacuum oleaners that customers may use for part of a day betore returning. The function f(x) = Gir +14 models the total rental cost af a vacuum cleanier. Which is a reasonable domain tor the function? A. \( 14

Ask by Phillips Burns. in the United States

Jan 22,2025

To determine the reasonable domain for the function \( f(x) = \text{Gir} + 14 \) (assuming a typo and interpreting it as \( f(x) = 5x + 14 \)), let's analyze the context: 1. **Understanding the Function:** - **\( f(x) \)** represents the total rental cost of the vacuum cleaner. - **\( x \)** is likely the number of hours the vacuum cleaner is rented. - The function suggests a base fee (\$14) plus an additional cost per hour (\$5 per hour). 2. **Determining the Domain:** - The rental period is described as "part of a day," which implies that the maximum rental time should not exceed 24 hours. - Therefore, **\( x \)** should be greater than 0 (since you can't rent for a negative amount of time) and less than or equal to 24 hours. - Among the provided options, **\( 0 < x < 25 \)** best fits this scenario, allowing for rentals up to just under 24 hours. 3. **Evaluating Other Options:** - **Option A (\( 14 < x < 32 \))**: This range doesn't make sense in the context of rental hours. - **Option C (\( 0 < x < 12 \))**: This restricts rentals to less than half a day, which might be too limiting. - **Option D (\( 14 < x < 86 \))**: This range exceeds the typical daily rental period by a significant margin. **Final Answer:** **Option B. \( 0 < x < 25 \)**