Pearl City Groceries offers unlimited grocery deliveries for a flat monthly fee of $10. The function 

C

(

m

)

 represents the cost, in dollars, of 

m

 months of grocery delivery.

What is the domain of 

C

(

m

)

?

To determine the domain of $ C(m) $, the function representing the cost of $ m $ months of grocery delivery for Pearl City Groceries, we need to understand what $ m $ represents and the constraints on its possible values.

Given:
- Pearl City Groceries charges a flat monthly fee of $10 for unlimited grocery deliveries.
- The function $ C(m) $ represents the cost in dollars for $ m $ months.

The function can be written as:
\[ C(m) = 10m \]

Here, $ m $ represents the number of months. In practical terms:
- $ m $ must be a non-negative integer because one cannot have a negative number of months.
- $ m $ could be zero if no months of service are used.

Thus, the domain of $ C(m) $ is all non-negative integers.

In set notation, this can be expressed as:
\[ \{ m \in \mathbb{Z} \mid m \geq 0 \} \]

This means $ m $ can be 0, 1, 2, 3, and so on.

Therefore, the domain of $ C(m) $ is:
\[ m \in \{0, 1, 2, 3, \ldots\} \]

Would you like more details on this solution or have any questions?

Here are some related questions to explore:

1. What is the range of the function $ C(m) $?
2. What is the total cost for 5 months of grocery delivery?
3. How much would Pearl City Groceries charge for 12 months of delivery?
4. If the monthly fee increases to $15, what will the new function $ C(m) $ be?
5. How does the total cost change if Pearl City Groceries offers a discount for 6 months of service?
6. What would be the cost function if the first month were free and subsequent months were charged $10 each?
7. How would you represent the cost if Pearl City Groceries offered a yearly subscription for $100 instead?
8. What is the average monthly cost if Pearl City Groceries offers a 10% discount on a yearly subscription?

**Tip:** When determining the domain of a function, always consider the context of the problem and whether the variable can take on non-integer values, negative values, or zero.

Understand the domain of the function C(m) that calculates the cost of m months of grocery delivery for Pearl City Groceries, which charges a flat monthly fee of $10. Learn how to determine the valid values for m and explore related questions about the cost function.

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