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The problem in the image describes a telephone company charging a flat rate of $30 per month with 200 free call minutes, after which the company charges $0.03 per minute.

### a) Write the function using function notation.

Let's define the function $ C(x) $, where $ C(x) $ represents the total monthly cost, and $ x $ is the total number of call minutes used in a month.

- For the first 200 minutes, the cost is fixed at $30.
- For any additional minutes beyond 200, there is an additional charge of $0.03 per minute.

Thus, the function can be written as:

\[
C(x) =
\begin{cases}
30 & \text{if } x \leq 200, \\
30 + 0.03(x - 200) & \text{if } x > 200.
\end{cases}
\]

This piecewise function represents the monthly charge based on the number of minutes used.

Do you need further clarification or details? 

### Related questions:
1. How would the function change if the charge per minute after 200 minutes was different?
2. What would the function look like if there was no fixed $30 monthly fee but only a per-minute charge?
3. How can this function be graphed, and what does the graph represent?
4. What happens to the total cost if a user makes exactly 200 minutes of calls?
5. How can we express this cost function using a single algebraic expression (without piecewise)?

### Tip:
When working with piecewise functions, always remember to carefully consider the boundary conditions, such as the point where the pricing changes from a flat rate to per-minute charges.

A telephone company charges $30 a month and gives the customer 200 free call minutes. After the 200 min, the company charges $0.03 a minute. a) Write the function using function notation.

Learn how to write a function for a telephone plan that charges $30 a month with 200 free call minutes and an additional $0.03 per minute over 200. This algebra problem involves piecewise functions, ideal for students in Grades 9-12.

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