Question

Children's cough syrup has dosage guidelines based on a child's age. In the following piecewise function, x represents te child's age in years and f(x) represents the dosage in fluid ounces.

Answer 1

It seems like you would like to create or interpret a piecewise function for children's cough syrup dosage based on age. Typically, this function would specify different dosage guidelines depending on the age ranges of the child. Here’s a generic example of what such a piecewise function might look like:

\[
f(x) =
\begin{cases}
0.5 & \text{if } 2 \leq x < 4 \\
1.0 & \text{if } 4 \leq x < 6 \\
1.5 & \text{if } 6 \leq x < 8 \\
2.0 & \text{if } 8 \leq x < 12 \\
2.5 & \text{if } 12 \leq x < 18 \\
\text{undefined} & \text{if } x < 2 \text{ or } x \geq 18
\end{cases}
\]

### Explanation of the Function:
- For children aged **2 to less than 4 years**, the dosage is **0.5 fluid ounces**.
- For children aged **4 to less than 6 years**, the dosage is **1.0 fluid ounce**.
- For children aged **6 to less than 8 years**, the dosage is **1.5 fluid ounces**.
- For children aged **8 to less than 12 years**, the dosage is **2.0 fluid ounces**.
- For children aged **12 to less than 18 years**, the dosage is **2.5 fluid ounces**.
- The dosage is **undefined** for children under **2 years** and those aged **18 years and older**.

### Important Considerations:
- Always consult a healthcare professional before administering any medication to children.
- These dosage guidelines can vary based on specific products or health recommendations, so it is essential to check the label or consult a physician.

If you have specific ranges or dosages in mind, feel free to share, and I can help you create a more tailored piecewise function!