A supermarket has a discount on "family packs" of meat. chicken cost  $2.00 per pound for packages over 5 pounds. smaller packages cost $2.50 per pound. write a piecewise function

We need to define a piecewise function that expresses the cost of chicken, $ C(x) $, based on the weight of the package $ x $ in pounds.

Here's how the problem breaks down:

- For packages that weigh more than 5 pounds, the price is $ 2.00 $ dollars per pound.
- For packages that weigh 5 pounds or less, the price is $ 2.50 $ dollars per pound.

The piecewise function is written as follows:

\[
C(x) =
\begin{cases}
2.50x & \text{if } 0 < x \leq 5 \\
2.00x & \text{if } x > 5
\end{cases}
\]

Where $ x $ is the weight of the chicken package in pounds.

This function takes into account the two different pricing rates, depending on whether the package is over 5 pounds or not.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you compute the total cost for a package weighing 4 pounds?
2. What would the cost be for a package that weighs 6 pounds?
3. How does the function change if the cutoff weight changes to 6 pounds?
4. Can you graph this piecewise function to see how the price per pound changes visually?
5. How can you represent this situation using inequalities?

**Tip**: Always check the domain of each part of a piecewise function to ensure you account for all possible values of the variable.

A supermarket has a discount on 'family packs' of meat. Chicken costs $2.00 per pound for packages over 5 pounds. Smaller packages cost $2.50 per pound. Write a piecewise function.

Understand how to write a piecewise function to calculate the cost of chicken based on package size. For packages over 5 pounds, the price is $2.00 per pound, while smaller packages cost $2.50 per pound. Suitable for students in Grades 8-10.

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