To determine why the sale price is a function of the original price, let's analyze the given data and check each of the provided statements in detail.
1. As the original price increases, the sale price also increases:
- We observe the original prices: \[tex]$7.99, \$[/tex]10.99, \[tex]$12.99, \$[/tex]15.99, \[tex]$24.99, \$[/tex]29.99.
- We see that these prices are in increasing order.
- We then look at the corresponding sale prices: \[tex]$5.59, \$[/tex]7.69, \[tex]$9.09, \$[/tex]11.19, \[tex]$17.49, \$[/tex]20.99.
- These prices are also in increasing order.
- Thus, it is true that as the original price increases, the sale price also increases.
2. The sale price is always less than the original price:
- We compare each pair of original and sale prices:
- \[tex]$7.99 > \$[/tex]5.59
- \[tex]$10.99 > \$[/tex]7.69
- \[tex]$12.99 > \$[/tex]9.09
- \[tex]$15.99 > \$[/tex]11.19
- \[tex]$24.99 > \$[/tex]17.49
- \[tex]$29.99 > \$[/tex]20.99
- In every case, the sale price is less than the original price.
3. For every original price, there is exactly one sale price:
- We list the original prices: \[tex]$7.99, \$[/tex]10.99, \[tex]$12.99, \$[/tex]15.99, \[tex]$24.99, \$[/tex]29.99.
- We list the corresponding sale prices: \[tex]$5.59, \$[/tex]7.69, \[tex]$9.09, \$[/tex]11.19, \[tex]$17.49, \$[/tex]20.99.
- Each original price pairs uniquely with one sale price without any repetitions or omissions.
- Therefore, this statement is true.
4. The sale price is never less than zero:
- The lowest sale price listed is \$5.59.
- All the sale prices are positive and none of them are negative or zero.
- Thus, the sale price is never less than zero.
Given these analyses:
- Statement 1: True
- Statement 2: True
- Statement 3: True
- Statement 4: True
All statements are true and valid in describing why the sale price is a function of the original price. However, the reason that best describes the relationship is:
"For every original price, there is exactly one sale price."
This is the defining property of a function, where each input (original price) is associated with exactly one output (sale price).
