Answer:
![f(x) = 1.2(\frac{x}{2})\text{ where, }120 \leq x \leq 240](https://tex.z-dn.net/?f=f%28x%29%20%3D%201.2%28%5Cfrac%7Bx%7D%7B2%7D%29%5Ctext%7B%20where%2C%20%7D120%20%5Cleq%20x%20%5Cleq%20240)
Step-by-step explanation:
Suppose she earns f(x) dollar by making sundaes in x minutes.
As per statement,
She just makes sundaes for a single shift of at most 4 hours and at least 2 hours,
⇒ She can make sundaes for a single shift of at most 240 minutes and at least 120 minutes, ( 1 hour = 60 minutes )
That is, 120 ≤ x ≤ 240
Now, She can prepare 1 sundae every 2 minutes,
Thus, for her,
2 minutes = 1 sundae
⇒ 1 minute = 1/2 sundae
⇒ She can prepare x/2 sundae every x minutes,
Also, she earns $1.20 for each sundae she makes.
Thus, her total earning in x minutes,
![f(x)=1.2(\frac{1}{2})\text{ Where, }120 \leq x \leq 240](https://tex.z-dn.net/?f=f%28x%29%3D1.2%28%5Cfrac%7B1%7D%7B2%7D%29%5Ctext%7B%20Where%2C%20%7D120%20%5Cleq%20x%20%5Cleq%20240)
Which is the required function that relates her earnings to the number of minutes she works.