A cell phone plan has a basic charge of $35 a month. The plan includes 400 free minutes and charges 10 cents for each additional minute of usage. Write the monthly cost C as a function of the number x of minutes used and graph C as a function of x for - is less than or equal to x is less than or equal to 600.

Here is the graph of the monthly cost $ C(x) $ as a function of the number of minutes used $ x $, for the range $ 0 \leq x \leq 600 $.

### Key Points:
- The cost is $35 for usage up to 400 minutes (indicated by the horizontal line).
- After 400 minutes, the cost increases by $0.10 for each additional minute (indicated by the sloped line).

### Do you want details or have any questions?

Here are five related questions for further exploration:
1. How much does the monthly cost increase when an additional 100 minutes are used after 400 minutes?
2. What is the cost if 500 minutes are used in a month?
3. How would the function change if the number of free minutes increased to 500?
4. What happens to the cost function if the per-minute charge is reduced to 5 cents?
5. How would you calculate the total cost for any number of minutes used if the base charge changes?

**Tip:** Piecewise functions are useful for modeling situations with different rules or conditions over specific intervals.

Explore the monthly cost function for a cell phone plan with a $35 basic charge, 400 free minutes, and a charge of $0.10 for each additional minute. Graph and analyze the cost function for different usage scenarios.

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