To determine which statement best describes why the sale price is a function of the original price, let's examine the relationship between the original prices and the sale prices from the given chart:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Original price} & \text{Sale price} \\
\hline
\$7.99 & \$5.59 \\
\hline
\$10.99 & \$7.69 \\
\hline
\$12.99 & \$9.09 \\
\hline
\$15.99 & \$11.19 \\
\hline
\$24.99 & \$17.49 \\
\hline
\$29.99 & \$20.99 \\
\hline
\end{array}
\][/tex]
The statements to consider are:
1. As the original price increases, the sale price also increases.
2. The sale price is always less than the original price.
3. For every original price, there is exactly one sale price.
4. The sales price is never less than zero.
Let's analyze each statement:
1. As the original price increases, the sale price also increases.
- Observing the table, it is true that the sale price increases as the original price increases. However, this isn't sufficient to define a function by the classic mathematical definition.
2. The sale price is always less than the original price.
- This is true based on the observations from the table. However, this condition alone does not define a functional relationship.
3. For every original price, there is exactly one sale price.
- This is the definition of a function. A function implies that each input (original price) has exactly one output (sale price). According to the table, every original price maps to one unique sale price, fulfilling the requirement of a function.
4. The sales price is never less than zero.
- While true, this statement is about a condition applying to sale prices, not about the functional relationship between original and sale prices.
Given the context and definition of a function in mathematics, the correct choice is:
For every original price, there is exactly one sale price.
This describes why the sale price is a function of the original price. Each original price has one and only one corresponding sale price, fitting the definition of a function perfectly. Therefore, the best statement to describe this relationship is:
For every original price, there is exactly one sale price.
