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:

$$f(x)=\{\begin{array}{lllllll}0.5& \text{if }2\le x<41.0& \text{if }4\le x<61.5& \text{if }6\le x<82.0& \text{if }8\le x<122.5& \text{if }12\le x<18\text{undefined}& \text{if }x<2\text{ or }x\ge 18\end{array}$$

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!