You buy x bottles of soda for $1.50 using a gift card that you got as a reward for getting good grades on your last report card. Your gift card's original balance was $15. The function represents the amount of money you have left on the card after your purchase. What is the domain of the function? Explain your reasoning.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Problem 3: Gift Card Balance**
You buy \( x \) bottles of soda for $1.50 each using a gift card that you got as a reward for getting good grades on your last report card. Your gift card’s original balance was $15. The function represents the amount of money you have left on the card after your purchase. What is the domain of the function? Explain your reasoning.
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**Explanation:**
To determine the domain of the function, consider the number of bottles of soda you can buy.
1. **Expression for Remaining Balance**:
The total cost for \( x \) bottles is \( 1.50x \).
The remaining balance on the card is \( 15 - 1.50x \).
2. **Domain Considerations**:
- The balance must remain non-negative:
\( 15 - 1.50x \geq 0 \).
- Solve for \( x \):
\( x \leq \frac{15}{1.50} \).
\( x \leq 10 \).
3. **Domain Result**:
Therefore, \( x \) must be a whole number from 0 to 10, inclusive.
The domain of the function is the set of whole numbers \([0, 10]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63e1e2a8-984c-41e4-9394-6eedd2f7212f%2Fab706c24-af51-4e0e-b8c5-42a5d65b3d2c%2Fjvi2fz_processed.jpeg&w=3840&q=75)
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