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

Question

UpStudy AI · Accepted Answer

To determine the reasonable domain for the function $$ f(x) = 	ext{Gir} + 14 $$ (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. $$ 0 < x < 25 $$**
The reasonable domain for the function is $$ 0 < x < 25 $$.

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

Real Tutor Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions

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