
Write a function for the situation and tell if the graph is continuous or discrete. Explain why it is continuous or discrete in your test work.

A movie store sells DVDs for $11 each. What is the cost, C, of n DVDs?

To model the situation of a movie store selling DVDs at $11 each, we can create a function that represents the total cost based on the number of DVDs purchased.

### Function:
Let:
- $ C $ be the total cost,
- $ n $ be the number of DVDs.

The cost of $ n $ DVDs at $11 each is given by the function:
\[
C(n) = 11n
\]
Where $ C(n) $ represents the total cost, and $ n $ is the number of DVDs bought.

### Graph Type: Continuous or Discrete?

This function represents a **discrete** graph. Here's why:

- **Discrete** means that the graph consists of isolated points rather than a continuous curve.
- In this context, the number of DVDs $ n $ can only take **whole number values** (e.g., 0, 1, 2, 3, ...), because you can't buy a fraction of a DVD.
- Therefore, the graph of this function will only include specific points, not a continuous line. Each point corresponds to a whole number $ n $ (such as 1 DVD, 2 DVDs, etc.), making the graph discrete.

### Conclusion:
The graph of the function $ C(n) = 11n $ is **discrete** because the number of DVDs $ n $ can only be whole numbers, and fractional or decimal values of DVDs do not make sense in this context.

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Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the function change if the price of each DVD were increased?
2. What if the store offered a discount for buying more than 5 DVDs—how would the function change?
3. Could you represent the total cost function if the store also charged a flat shipping fee?
4. How would the graph look if DVDs could be sold in fractions, like streaming credits?
5. What is the cost of buying 0 DVDs? How does the function handle this?

**Tip:** When working with discrete graphs, always check whether the context allows for fractional or decimal values!

A movie store sells DVDs for $11 each. What is the cost, C, of n DVDs? Write a function for the situation and tell if the graph is continuous or discrete. Explain why it is continuous or discrete in your test work.

Learn how to create a cost function C(n) = 11n for DVDs sold at $11 each. Understand why the graph is discrete and how whole-number quantities affect the function. Perfect for students in Grades 6-8 studying linear and discrete functions.

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