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.