https://file.aiquickdraw.com/mathbot/file/17295347493827ohema1p.jpg

Let's break down the problem in the image:

We are asked to find the range of the function $ y $, which represents the daily cost of hiring a lawn service for $ x $ hours. The function given is linear, and the problem gives us:

- A fixed cost of $100
- An additional cost of $25 per hour
- The maximum number of hours the lawn service can work is 6 hours per day.

The cost function $ y(x) $ can be written as:
\[
y = 100 + 25x
\]
Where $ x $ is the number of hours worked, and the lawn service works for a maximum of 6 hours, so $ 0 \leq x \leq 6 $.

### Finding the range of $ y $:
1. When $ x = 0 $ hours (minimum), the cost is:
   \[
   y = 100 + 25(0) = 100
   \]
2. When $ x = 6 $ hours (maximum), the cost is:
   \[
   y = 100 + 25(6) = 100 + 150 = 250
   \]

Thus, the range of the function is $ 100 \leq y \leq 250 $.

### Correct Answer:
The correct answer is **b. $ 100 \leq y \leq 250 $**.

Would you like further details or have any other questions?

---

Here are 5 related questions you might consider:
1. How do you find the range of a function from its equation?
2. How would the range change if the fixed cost increased?
3. What if the cost per hour was $30 instead of $25? How would that affect the range?
4. How do you interpret the domain and range in a real-life situation like this?
5. What are the differences between linear and non-linear cost functions?

**Tip**: Always look at the domain first when asked to find the range of a function, especially in practical scenarios.

The daily cost of hiring a lawn service, y, to work x hours mowing the grounds on a golf course can be modeled using a linear function. The lawn service charges a fixed cost of $100, plus an additional cost of $25 per hour. The lawn service works a maximum of 6 hours per day. For one day of work, what is the range of the function for this situation?

Learn how to determine the range of the linear function representing the daily cost of hiring a lawn service for up to 6 hours. This problem involves calculating costs using a fixed rate and a per-hour charge, suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation